CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

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 = a_n – a_n-1. S_n is sum upto n terms in this sequence and a₃ = 5. How many values m, n exist such than S_m – S_n = 65?

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

Video Explanation

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
S_n = n²
S_m – S_n
=> 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 = a_n – a_n-1. S_n is sum upto n terms in this sequence and a₃ = 5. How many values m, n exist such than S_m – S_n = 65? "

Hence the answer is "2"

Choice C is the correct answer.