Question

The first and last term of an ap are a and l respectively isf s be the sum of all the terms of the ap show that coomon diffrence is l square-a square /2s-(l+a)

Answer 1

Step-by-step explanation:

Given:

a = a, aₙ = l, Sₙ = s

To Prove:

d = (l²- a²)/[2s - (l + a)]

Proof⇒

Sₙ = (n/2) [a+l}

⇒ 2s = n (l + a)

⇒ n =2s/ (l+a)   ...(1)

Now, l = a + (n-1)d

⇒ d = (l - a)/(n - 1)

Substitute (1) here to get⇒ d = (l + a)(l - a)/[2s - (l + a)]

⇒ d = (l²- a²)/[2s - (l + a)]

                                                                      Hence Proved!