Question

Find the sum 25 + 28 + 31 + .+ 100.

Answer 1

Here, a = 25, d = (28 − 25) = 3 and l = 100
Let there be n terms in the given AP.
Then T_n = 100
⇒ a + (n − 1)d = 100
⇒ 25 + (n − 1)⨯​3 = 100
⇒ 3n = 78
⇒ n = 26

Sum of n terms of an AP is given by
$$\begin{gathered} S_n=\frac{n}{2}\left[a+l\right] \\ =\frac{26}{2}\left[25+100\right] \\ =13\times 125=1625 \end{gathered}$$