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CAT Questions | Algebra | Polynomials - Sequence

The question is from Sequences. The Question involves finding possible values of m and n. We need to find out the possible values, that satisfy the conditions of the sequence. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 11: A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65?

  1. 4
  2. 6
  3. 2
  4. More than 6 possibilities

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: An arithemetic progression in the form of a sequence!

a3 = 5, a4 = 7, a5 = 9, a2 = 3, a1 = 1
So, the sequence is nothing but 1, 3, 5, 7, 9....
S1 = 1
S2 = 4
S3 = 9
S4 = 16
Sn = n2
Sm – Sn
=> m2 – n2 = 65
=> (m + n) ( m – n) = 65, m, n are natural numbers.
=> This could be 65 * 1 or 13 * 5. Two possibilities. Note that this cannot be written as 1 * 65 or 5 * 13 as m + n > m - n {as m, n are natural numbers}

The question is "A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65? "

Hence the answer is "2"

Choice C is the correct answer.

 


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