Question

If in an AP the value of qth term is 115 and the sum of first p term is 4p²- p. Find the value of q.
1. 17
2. 13
3. 15
4. None of these

Answer 1

Correct Answer - Option 3 : 15

Given ∶

The value is qth term is 115.

Sum of p terms = 4p2- p.

Formula Used∶

A_n= S_n - S_n-1 

Basics of Arithmetic progression.

Calculation∶

It is given that, S_p = 4p² - p

Sum of q terms, S_q = 4q² - q

Sum of q - 1 terms, S_q-1 = 4(q - 1)² - (q - 1)

So, qth term, a_q = S_q - S_q-1

a_q = 4q²- q - [ 4(q -1)² - (q -1)]

⇒ a_q = 4q²- q - [4q² + 4 - 8q - q + 1]

⇒ a_q = 8q - 5 

But a_q = 115

⇒ 115 = 8q - 5

⇒ 8q = 120

⇒ q = 15

∴ The required value q is 15.