Question

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by: l2 - a2 / k - (l+a). Then k = ? Please answer me fast.

Answer 1

This is the required answer and it is hard to understand. SO if not understood plz do ask me. The answer is 2S

Answer 2

k = 2S

Step-by-step explanation:

common difference is given by =  (l² - a²) /(k - (l + a))

First Term = a

Last term = l

let say total terms = n

& Common difference = d

=> l = a + (n - 1)d

=> (n - 1) = (l - a)/d

=> n = (l - a)/d  + 1

Sum of n terms

S = (n/2)(a + l)

=> n = 2S/(a + l)

2S/(a + l) = (l - a)/d  + 1

=> 2S = (l² - a²)/d  + a + l

=> (l² - a²)/d = 2S - a - l

=> d =  (l² - a²) /(2S - a - l)

=> d =  (l² - a²) /(2S - (a + l))

=> d =  (l² - a²) /(2S - (l + a))

d = (l² - a²) /(k - (l + a))   given

Comparing

=> k = 2S

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