Question

Find the sum of first 26 terms of the AP 1, 3, 5, 7, ..... .

Answer 1

Here, a = 1, d = (3-1) = 2 and n = 26
Using the formula, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$, we get:
$$\begin{gathered} S_{26}=\frac{26}{2}\left[1\times 2+\left(26-1\right)2\right][\because a=1,d=2\mathrm{and}n=26] \\ =13\times \left[2+50\right]=13\times 52=676 \end{gathered}$$

Hence, the sum of the first 26 terms of the given AP is 676.