Question

The 11th term of the AP −3, $\frac{-1}{2},2,....$ is
(a) 22
(b) 28
(c) −38
(d) $48\frac{1}{2}$

Answer 1

(a) 22
The given AP is -3, $-\frac{1}{2}$, 2, ...
Here, first term, a = -3 and common difference, d = $\left[-\frac{1}{2}-\left(-3\right)\right]=\left[3-\frac{1}{2}\right]=2\frac{1}{2}$
$$\begin{gathered} \mathrm{Now},T_{11}=a+\left(11-1\right)d=a+10d \\ =-3+10\times \left(2\frac{1}{2}\right)=-3+\left(10\times \frac{5}{2}\right)=-3+25=22 \end{gathered}$$

∴ 11^th term = 22