Question

The first term of an A.P. of a consecutive integer is p^+1. The sum of (2p+1) terms of this series can be expressed as?

Answer 1

$<b>$ SOLUTION

The formula for finding the sum to the nth term of an AP is

Sn = n/2(2a+(n-1)d)

In this question:

a = p² + 1

d = 1 (They are consecutive integers)

n = 2p + 1



Substitute these in the above formula

Sn = (2p+1)/2{2(p² + 1) + (2p+1 -1)(1)}

Sn = (2p+1)/2{2p² + 2 + 2p}

Sn = (2p+1)(p²+p+1)

Sn = 2p³ + 3p² + 1