Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The first term of an A.P of consecutive integers is p2 + 1. The sum of (2p + 1) terms of this series can be expressed as

(1) (P + 1)2

(2) (p + 1)3

(3) (2p + 1)(p + 1)2

(4) p3 + (p + 1)3

Solution:

Given first term of AP, a = p2+1

Here d = 1, since integers are consecutive.

Sum of first n terms of AP, Sn = (n/2)(2a+(n-1)d)

S2p+1 = ((2p+1)/2)(2a+(2p+1-1)d)

= ((2p+1)/2)(2(p2+1)+2p)

= (2p+1)(p2+1+p)

= 2p3+p2+2p+1+2p2+p

= p3 + p3 + 3p2+ 3p +1

= p3 + (p+1)3

Hence option (4) is the answer.

Was this answer helpful?

 
   

4 (16)

(29)
(3)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

Ask
Question