Question

If the nth term of an AP is 2n+1, then the sum of first n
terms of an AP is:

Answer 1

$\mathfrak \blue{ \underline{here \: is \: your \: answer :}} \\ a_{n} = 2n + 1 \: \\ too \: find \: : s_{n} = ? \\ solve : a_{n} = 2n + 1 \\ a_{1} = 2(1)+ 1 \\ a_{1} = 3 \\ so... \\ s_{n} = \frac{n}{2} (a + a_{n}) \\ s_{n} = \frac{n}{2} (3 + 2n + 1) \\ s_{n} = \frac{n}{2} (4 + 2n) \\ s_{n} = \frac{n}{2} (2(2 + n)) \\ s_{n} = 2n + {n}^{2}$

Hope my answer will help you..