An arithmetic progression has 15 terms. Its 8thterm is 8. If S is the sum of its terms, then whichof the following is true?(1) S 100(2) S = 100(3) S (4) None of these

Number of terms, n = 15
Suppose a be the first term and d be the common difference of an A.P.
We know that nth term of an A.P. is $t_n = a+\left(n-1\right)d$
So 8th term of an A.P. = $t_8 = a+\left(8-1\right)d = 8$
$\Rightarrow a+7d = 8 ...\left(\mathrm{i}\right)$
Sum of 15 terms of an A.P. = $\frac{15}{2}\left[2a+\left(15-1\right)d\right]$ = S
$$\begin{gathered} \Rightarrow \frac{15}{2}\left[2a+14d\right] = S \\ \Rightarrow \frac{15}{2}\times 2\left(a+7d\right) = S \\ \Rightarrow S= 15\times 8 = 120 \{\mathrm{using} (i\left)\right\} \end{gathered}$$
so the value of S = 120