In an A.P., if the first term $a = 7$, $n$th term $a_n = 84$ and the sum of first $n$ terms $s_n = \frac{2093…

Question

In an A.P., if the first term $a = 7$, $n$th term $a_n = 84$ and the sum of first $n$ terms $s_n = \frac{2093}{2}$, then $n$ is equal to :

Accepted Answer

## Model Answer Using $S_n = \dfrac{n}{2}(a + a_n)$: $$\frac{2093}{2} = \frac{n}{2}(7 + 84) = \frac{91n}{2} \implies n = \frac{2093}{91} = 23$$ **(c) 23** ## Explanation Use the shortcut formula $S_n = \frac{n}{2}(a + l)$ when first term, last term, and sum are all given. Dividing 2093 by 91 directly gives n = 23. No need to find d separately.

Mathematics — CBSE Class 10 board question