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CAT Quantitative Aptitude | CAT Algebra: Progressions Questions

A CAT Algebra question from Progressions that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts from Number Theory and Algebra. It involves concepts based on Artihmetic Progressions and Geometric Progressions. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with the following questions. In CAT Exam, one can generally expect to get 1~2 questions from Progressions. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

  1. CAT Progressions - Geometric Progressions

    Second term of a GP is 1000 and the common ratio is r = \\frac{1}{n}\\) where n is a natural number. Pn is the product of n terms of this GP. P6 > P5 and P6 > P7, what is the sum of all possible values of n?

    1. 4
    2. 9
    3. 5
    4. 13
    Choice B
    9

  2. CAT Progressions - Common Ratio

    Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the same GP. Sum of the first 17 terms is 92, what is the third term in the GP?

    1. 92
    2. -92
    3. 46
    4. 231
    Choice A
    92

  3. CAT Progressions - Sum up to 'n' Terms

    Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

    1. \\frac{8}{25}\\)
    2. \\frac{4}{25}\\)
    3. \\frac{6}{25}\\)
    4. \\frac{1}{25}\\)
    Choice A
    \\frac{8}{25}\\)

  4. CAT Progressions - Common Difference

    Let the nth term of AP be defined as tn, and sum up to 'n' terms be defined as Sn. If |t8| = |t16| and t3 is not equal to t7, what is S23?

    1. 23(t16 - t8)
    2. 0
    3. 23t11
    4. Cannot be determined
    Choice B
    0

  5. CAT Progressions - Mean

    a, b, c, d and e are 5 distinct numbers that from an arithmetic progression. They are not necessarily consecutive terms but form the first 5 terms of the AP. It is known that c is the arithmetic mean of a and b, and d is the arithmetic mean of b anc c. Which of the following statements are true?
    i. Average of all 5 terms put together is c.
    ii. Average of d and e is not greater than average of a and b.
    iii. Average of b and c is greater than average of a and d.

    1. i and ii only
    2. ii and iii only
    3. all three statements are true
    4. i and iii only
    Choice A
    i and ii only

  6. CAT Progressions - Median

    Consider a, b, c in a G.P. such that |a + b + c| = 15. The median of these three terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this G.P.?

    1. 40000
    2. 32000
    3. 8000
    4. 48000
    Choice A
    40000

  7. CAT Progressions - Arithmetic Progressions

    If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P., what is 13 times the 13th term of this A.P.?

    1. 7 times the 13th term
    2. 0
    3. 13 times the 7th term
    4. 4 times the 4th term + 9 times the 9th term
    Choice B
    0

  8. CAT Progressions - Arithmetic Progressions

    Sequence P is defined by pn = pn-1 + 3, p1 = 11, Sequence Q is defined as qn = qn-1 – 4, q3 = 103. If pk > qk+2, what is the smallest value k can take?

    1. 6
    2. 11
    3. 14
    4. 15
    Choice D
    15

  9. CAT Progressions - Arithmetic Progressions

    The sum of 2n terms of A.P. {1, 5, 9, 13…..} is greater than sum of n terms of A.P. = {56, 58, 60..…}. What is the smallest value n can take?

    1. 9
    2. 10
    3. 12
    4. 14
    Choice A
    9

  10. CAT Progressions - Arithmetic Progressions

    a, b, c and d are in A.P., What can we say about terms bcd, acd, abd and abc?

    1. They are also in A.P.
    2. They are also in H.P.
    3. They are also in G.P.
    4. They are not in an A.P., G.P. or H.P.
    Choice B
    They are also in H.P.

  11. CAT Progressions - Arithmetic Progressions

    Second term in an AP is 8 and the 8th term is 2 more than thrice the second term. Find the sum up to 8 terms of this AP.

    1. 124
    2. 108
    3. 96
    4. 110
    Choice A
    124

  12. CAT Progressions - Sum of infinite terms

    If Sn = n3 + n2 + n + 1 , where Sn denotes the sum of the first n terms of a series and tm= 291, then m is equal to?

    1. 24
    2. 30
    3. 26
    4. 20
    Choice B
    30

  13. CAT Progressions - Sum of infinite terms

    Sum of infinite terms of a GP is 12. If the first term is 8, what is the 4th term of this GP?

    1. \\frac{8}{27}\\)
    2. \\frac{4}{27}\\)
    3. \\frac{8}{20}\\)
    4. \\frac{1}{3}\\)
    Choice A
    \\frac{8}{27}\\)

  14. CAT Progressions - Sum of a Sequence

    Find sum : 22 + 2 * 32 + 3 * 42 + 4 * 52.....10 * 112

    1. 6530
    2. 3600
    3. 2850
    4. 3850
    Choice D
    3850

  15. CAT Progressions - Ratio of Amounts

    The salaries earned by two friends Anil and Jeetu in different years are in A.P. If the ratio of the amount earned by them in ‘p’ number of years are (4p+1) : (2p+17). Then find the ratio of amount earned by them in the 7th year.

    1. (2p+1) : (4p+6)
    2. 53 : 43
    3. 4 : 7
    4. 15p : 36p
    Choice B
    53 : 43

  16. CAT Progressions - Arithmetic Progressions

    Ram invests a total sum of 2000 rupees on government bonds in 4 years. If these investments are in A.P and the sum of squares of the investments is 1200000. Find the investment made by ram in each year respectively. It is also known that he always invest more than the previous year.

    1. 200,400,600,800
    2. 875,625,375,125
    3. 125,375,625,875
    4. 50,350,650,950
    Choice A
    200,400,600,800

  17. CAT Progressions - Arithmetic Progressions

    Ram invest different amounts during the year on shares. S1, S2, S3……….Sm are different sums of ‘n’ amounts invested in ‘m’ years. If the amounts invested during the years are in A.P whose first terms are 1,2,3…..m and common difference are 1,3,5…..,(2m-1) respectively then find the total amount invested by Ram in ‘m’ years.

    1. n(m+1)
    2. m+1
    3. \\frac{mn}{2}\\)(mn+1)
    4. cannot be determined
    Choice C
    \\frac{mn}{2}\\)(mn+1)

  18. CAT Progressions - Sequence and Series

    Find the sum of the series .4 + .44 + .444……. to n terms

    1. 5.69
    2. 14.44
    3. \\frac{4}{81}\\)[9n-1+\\frac{1}{10^n}\\)]
    4. \\frac{4}{81}\\)[n + 1]
    Choice C
    \\frac{4}{81}\\)[9n-1+\\frac{1}{10^n}\\)]

  19. CAT Progressions - A.P, G.P and H.P

    If the equation px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common root,
    then in which type of progression is \\frac{d}{p}\\) , \\frac{e}{q}\\) , \\frac{f}{r}\\)

    1. \\frac{d}{p}\\) , \\frac{e}{q}\\) , \\frac{f}{r}\\) are in G.P
    2. \\frac{d}{p}\\) , \\frac{e}{q}\\) , \\frac{f}{r}\\) are in A.P
    3. \\frac{d}{p}\\) , \\frac{e}{q}\\) , \\frac{f}{r}\\) are in H.P
    4. Insufficient Data
    Choice B
    \\frac{d}{p}\\) , \\frac{e}{q}\\) , \\frac{f}{r}\\) are in A.P

  20. CAT Progressions - Sum of all Terms

    Find the sum of all the terms, If the first 3 terms among 4 positive integers are in A.P and the last 3 terms are in G.P. Moreover the difference between the first and last term is 40.

    1. 108
    2. 172
    3. 124
    4. 196
    Choice B
    172

  21. The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

    IPMAT Rohtak Sample Paper Mock
    IPMAT Indore Sample Paper Mock

    Please note that the explanation button will take you to the IPMAT solution page.


  22. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Sequences

    What should come at the place of question mark? 46080, 3840, 384, 48, 8, 2, ?

    1. 1
    2. \\frac{1}{64}\\)
    3. \\frac{1}{8}\\)
    4. None of these
    Choice A
    1

  23. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Progressions

    The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

    1. 44
    2. 22
    3. 19
    4. None of the above
    Choice A
    44

  24. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Progressions

    Given A = 265 and B = (264 + 263 + 262 + ... + 20), which of the following is true?

    1. B is 264 larger than A
    2. A and B are equal
    3. B is larger than A by 1
    4. A is larger than B by 1
    Choice D
    A is larger than B by 1

  25. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Progressions

    If log 2, log (2x - 1) and log (2x + 3) are in A.P, then x is equal to ____

    1. \\frac{5}{2}\\)
    2. log25
    3. log32
    4. 32
    Choice A
    \\frac{5}{2}\\)

  26. IPMAT 2019 Question Paper - IPM Indore Quants,Progressions

    If x, y, z are positive real numbers such that x12 = y16 = z24,and the three quantities 3logyx, 4logzy, nlogxz are in arithmetic progression, then the value of n is

    16

  27. IPMAT 2019 Question Paper - IPM Indore Quants,Progressions

    Let \\alpha, \beta\\) be the roots of x2 - x + p = 0 and \\gamma, \delta\\) be the roots of x2 - 4x + q = 0 where p and q are integers. If \\alpha, \beta, \gamma, \delta\\) are in geometric progression then p + q is

    1. -34
    2. 30
    3. 26
    4. -38
    Choice A
    -34

  28. IPMAT 2019 Question Paper - IPM Indore Quants,Progressions

    The number of terms common to both the arithmetic progressions 2,5,8,11,...., 179 and 3,5,7,9,....., 101 is

    1. 17
    2. 16
    3. 19
    4. 15
    Choice A
    17

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.


  1. CAT 2017 Question Paper Slot 1 - Progressions

    If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is:

    1. 2 : 3
    2. 3 : 2
    3. 3 : 4
    4. 4 : 3
    Choice A
    2 : 3

  2. CAT 2017 Question Paper Slot 1 - Progressions

    Let a1, a2,.......a3n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ......+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + ..... + an) > 1830?

    1. 8
    2. 9
    3. 10
    4. 11
    Choice B
    9

  3. CAT 2017 Question Paper Slot 2 - Progressions

    Let a1, a2, a3, a4, a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3. If the sum of the numbers in the new sequence is 450, then a5 is [TITA]

    51

  4. CAT 2017 Question Paper Slot 2 - Progressions

    An infinite geometric progression a1, a2, a3,... has the property that an = 3(an+1 + an+2 +....) for every n ≥ 1. If the sum a1 + a2 + a3 +...... = 32, then a5 is

    1. \\frac{1}{32})
    2. \\frac{2}{32})
    3. \\frac{3}{32})
    4. \\frac{4}{32})
    Choice C
    \\frac{3}{32})

  5. CAT 2017 Question Paper Slot 2 - Progressions

    If a1 = \\frac{1}{2 × 5}) , a2 = \\frac{1}{5 × 8}) , a3 = \\frac{1}{8 × 11}),...., then a1 + a2 + a3 + ...... + a100 is

    1. \\frac{25}{151})
    2. \\frac{1}{2})
    3. \\frac{1}{4})
    4. \\frac{111}{55})
    Choice A
    \\frac{25}{151})

  6. CAT 2018 Question Paper Slot 1 - Sequence & Series

    Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

    1. \\frac{1}{6})
    2. \\frac{3}{6})
    3. \\frac{3}{2})
    4. \\frac{5}{2})
    Choice D
    \\frac{5}{2})

  7. CAT 2018 Question Paper Slot 2 - Sequence & Series

    Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

    1. 48
    2. 20
    3. 45
    4. 23
    Choice D
    23

  8. CAT 2018 Question Paper Slot 2 - Sequence & Series

    Let t1, t2,… be real numbers such that t1+ t2 +... + tn = 2n2 + 9n + 13, for every positive integer n ≥ 2. If tk=103, then k equals (TITA)

    24

  9. CAT 2018 Question Paper Slot 2 - Sequence & Series

    The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ..... + 95 x 99 is

    1. 80707
    2. 80751
    3. 80730
    4. 80773
    Choice A
    80707

  10. CAT 2018 Question Paper Slot 2 - Progressions & Series

    The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = \\frac{(x+y)}{2}\\) and v = \\frac{(y+z)}{2}\\). If x ≥ z, then the minimum possible value of x is (TITA)

    105

  11. CAT 2019 Question Paper Slot 1 - Progressions

    If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

    1. (1003)15 + 6
    2. (977)15 - 3
    3. (1003)215 - 3
    4. (977)214 + 3
    Choice C
    (1003)215 - 3

  12. CAT 2019 Question Paper Slot 1 - Progressions

    If a1 + a2 + a3 + ... + an = 3(2n+1 - 2), then a11 equals [TITA]

    6144

  13. CAT 2019 Question Paper Slot 1 - Progressions

    If a1, a2, ......... are in A.P , \\frac{1}{\sqrt{a_1} + \sqrt{a_2}}) + \\frac{1}{\sqrt{a_2} + \sqrt{a_3}}) + ......... + \\frac{1}{\sqrt{a_n} + \sqrt{a_{n+1}}}) then , is equal to

    1. \\frac{n}{\sqrt{a_1} + \sqrt{a_{n+1}}})
    2. \\frac{n - 1}{\sqrt{a_1} + \sqrt{a_n}})
    3. \\frac{n}{\sqrt{a_1} - \sqrt{a_{n+1}}})
    4. \\frac{n - 1}{\sqrt{a_1} + \sqrt{a_{n-1}}})
    Choice A
    \\frac{n}{\sqrt{a_1} + \sqrt{a_{n+1}}})

  14. CAT 2019 Question Paper Slot 2 - Sequence & series

    Let a1 , a2 be integers such that a1 – a2 + a3 – a4 + ........ +(-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals

    1. -1
    2. 1
    3. 0
    4. 10
    Choice B
    1

  15. CAT 2019 Question Paper Slot 2 - Sequence & series

    The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is

    1. 20
    2. 18
    3. 21
    4. 19
    Choice A
    20

  16. CAT 2019 Question Paper Slot 2 - Sequence & series

    If (2n+1) + (2n+3) + (2n+5) + ... + (2n+47) = 5280 , then what is the value of 1+2+3+ ... +n ? [TITA]

    4851


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