Question

If the sum of first n terms of an A.P. is an^2+bn, find its common difference.

Answer 1

If $S_{n}$=a$n^{2}$+bn 
To Find $T_{n} = S_{n} - S_{n-1}$
∴$T_{n}$=a($n^{2} - (n-1)^{2}$)+b
= a(2n-1)+b
and d=$T_{n} - T_{n-1}$
∴d=a(2n-1)+b -(a(2n-3)+b)=2a 
therefore common difference d=2a 

Answer 2

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