Question

If a = 8, T_n = 63 and S_n = 210, find the value of n.

Answer 1

Here, a = 8, T_n = 62 and S_n = 210
Now, a + (n − 1)d = 62
⇒ 8 + (n − 1)d = 62
⇒ (n − 1)d = 54

$$\begin{gathered} \mathrm{Now},S_n=\frac{n}{2}\left[2a+(n-1)d\right]=210\left[\mathrm{As}(n-1)d=55\right] \\ \Rightarrow \frac{n}{2}\left[2\times 8+54\right]=210 \\ \Rightarrow 70n=210\times 2 \\ \Rightarrow n=6 \end{gathered}$$