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# The sum of n terms of an AP is

Question:

The sum of $n$ terms of an $A P$ is $\frac{1}{2}$ an $^{2}+b n$. Find the common difference.

Solution:

Given: the sum of $n$ terms of an AP is $\frac{1}{2} a n^{2}+b n$

To find: common difference.

Put n = 1 we get

First term $=\frac{1}{2}+b$

Put n = 2 we get

First term + second term = 2 × a + 2 × b

Second term $=\frac{3}{2} a+b$

Therefore common difference will be

Second term - first term

Common difference $=2 \mathrm{a}$