# CAT Questions | CAT Algebra Questions

###### 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.

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 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 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. $\frac{1}{25}\\$ 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

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

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

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

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

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

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.

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

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

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. $\frac{1}{3}\\$ 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 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

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

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

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] 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, and p,q,r are in G.P., 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 20. #### CAT Progressions - Sum of all Terms Find the sum of all the terms, If the first 3 terms among 4 positive 2-digit 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 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 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 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

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. 8
2. 9
3. 10
4. 11

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]

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

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

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)

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

12. #### CAT 2019 Question Paper Slot 1 - Progressions

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

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

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

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]

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