Question

The sum of first 20 terms of the AP 1, 3, 5, 7, 9, ... is
(a) 264
(b) 400
(c) 472
(d) 563

Answer 1

(b) 400

Here, a = 1, d = (3 - 1) = 2 and n = 20
Using the formula, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$, we get:
$$\begin{gathered} S_{20}=\frac{20}{2}\left[2\times 1+\left(20-1\right)\times 2\right][\because a=1,d=2\mathrm{and}n=20] \\ =10\times \left[2+38\right]=10\times 40=400 \end{gathered}$$
Hence, the sum of the first 20 terms of the given AP is 400.