Question

The sum of n terms of an A.P. is n^2, Find the common difference

Answer 1

Answer:

We know that sum of n terms of an AP is

(n/2)[2a + (n – 1)d] , where a is the first term & d is the common difference of the AP.

It is given that sum of an AP is n2 .

So n2  = (n/2)[2a + (n – 1)d]  

i.e. n = a + (n – 1)d / 2

Put n = 1  ,  1 = a

Put n = 2  ,  2 = a + d / 2   i.e.  2 = 1 + d/2

\therefore d = 2  

The common difference of the given AP is 2.

Answer 2

Answer:

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