Question

The first term of an ap of consecutive integers is p^2 + 1. then find the sum of 2p + 1 terms of this series

Answer 1

The first term of an AP of consecutive integers is p² + 1
here we have to notice question use consecutive integers , it means, common difference is 1 .
So, a = p² + 1 and d = 1

Use formula,
Sn = n/2[2a + (n -1)d ]
Here, n = 2p + 1 , a = p² + 1 and d = 1
∴ sum of (2p + 1) terms = (2p + 1)/2 [2p² + 2 + (2p + 1 - 1) × 1 ]
= (2p + 1)/2 [2p² + 2 + 2p]
= (2p + 1)(p² + p + 1)

Hence, sum of (2p + 1) terms in AP = (2p + 1)(p² + p + 1)

Answer 2

here is ur answer ⤴⤴

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