Question

The first term of an AP of consecutive integers is p² + 1. The sum of 2p + 1 terms of this AP is ______.

Options

• (p + 1)²

• (2p + 1) (p + 1)²

• (p+1)³

• p³ + (p + 1)³

Answer 1

The first term of an AP of consecutive integers is p² + 1. The sum of 2p + 1 terms of this AP is p³ + (p + 1)³.

Explanation:-

∵ a = p² +1 and d = 1

`S_(2p+1)=(2p+1)/2(2p^2+2+(2p)1)`

`=(2p+1)/2(2)(p^2+p+1)`

= (2p + 1)(p² + p + 1)

= p³ + (p + 1)³