Question

the 1st term of an A.P of Consecutive integer is p2+1.the sum of (2p+1) terms of this series can be expressed as..?​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

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

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

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