(a) In an A.P., the first term is 32 and the last term is - 10. If the common difference is -2, then find the number of terms and their sum.

Here \(\displaystyle \mathrm{a}=32, l=-10\) and \(\displaystyle \mathrm{d}=-2\)

\[\begin{aligned} & \therefore 32+(\mathrm{n}-1)(-2)=- \\ & \Rightarrow \mathrm{n}=22 \\ & \mathrm{~S}_{22}=\frac{22}{2} \times[32+(-10)] \\ & \quad=242 \end{aligned} \]

\[\begin{aligned} & \mathrm{a}_{1}=3(1)-2=1 \\ & \text { and } \mathrm{a}_{28}=3(28)-2=82 \\ & \begin{aligned} \mathrm{S}_{28} & =\frac{28}{2} \times(1+82) \\ & =1162 \end{aligned} \end{aligned} \]