In an A.P., the first term is $32$ and the last term is $-10$. If t...

Question

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.

Accepted Answer

Step 1: Given $a = 32$, $a_n = -10$, $d = -2$.
Step 2: Use $a_n = a + (n-1)d$.
$$-10 = 32 + (n-1)(-2)$$
Step 3: $$-42 = -2(n-1) \Rightarrow n - 1 = 21 \Rightarrow n = 22$$
Step 4: Sum of $n$ terms $$S_n = \frac{n}{2}(a + a_n)$$
Step 5: $$S_{22} = \frac{22}{2}(32 + (-10)) = 11 	imes 22 = 242$$
Hence, number of terms $= 22$ and their sum $= 242$.

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