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in Arithmetic Progression by (30.9k points)
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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 \(\frac{1^2 - a^2}{K - (1 + a)}\), then k =

A. S 

B. 2S 

C. 3S 

D. none of these

1 Answer

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Best answer

Correct answer is B. 2S

Let the common difference and number of terms of AP be d and n respectively. 

Last term of AP = an = l (given) 

l = a + (n–1) d

D = \(\frac{(a + l)(a-l)}{2s - (L + a)}\)

Comparing this with \(\frac{1^2 -a^2}{K - (1 +a)}\)

We get k =2S

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