Question

Which term of the A.P. $-2,-7,-12,....$will be $-77$ ? Find the sum of this A.P. upto the term $-77$ .

Answer 1

Here, a = −2 and d = −5.
$$\begin{gathered} If{a}_n=-77. \\ \Rightarrow \left(-2\right)+\left(n-1\right)\left(-5\right)=-77 \\ \Rightarrow -2-5n+5=-77 \\ \Rightarrow n=16 \\ Therefore, \\ {S}_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right] \\ \Rightarrow S_{16}=\frac{16}{2}\left[2\left(-2\right)+\left(16-1\right)\left(-5\right)\right] \\ =8\left[-4-75\right] \\ =-632 \end{gathered}$$