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 a_{3} = 5. How many values m, n exist such than S_{m} – S_{n} = 65?

- 4
- 6
- 2
- More than 6 possibilities

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a_{3} = 5, a_{4} = 7, a_{5} = 9, a_{2} = 3, a_{1} = 1

So, the sequence is nothing but 1, 3, 5, 7, 9....

S_{1} = 1

S_{2} = 4

S_{3} = 9

S_{4} = 16

S_{n} = n^{2}

S_{m} – S_{n}

=> m^{2} – n^{2} = 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 a_{3} = 5. How many values m, n exist such than S_{m} – S_{n} = 65? "**

Choice C is the correct answer.

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