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.
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Given: $a = 32$, $l = -10$, $d = -2$
Finding n:
Using $a_n = a + (n-1)d$:
$$-10 = 32 + (n-1)(-2)$$
$$-42 = -2(n-1)$$
$$n - 1 = 21 \Rightarrow n = 22$$
Finding Sum:
$$S = \frac{n}{2}(a + l) = \frac{22}{2}(32 + (-10)) = 11 \times 22 = 242$$
∴ Number of terms = 22 and Sum = 242
Source: Chapter 5, Summary (points 3 and 5)
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Explanation
- Use $a_n = a + (n-1)d$ to find $n$ first (since last term $= a_n$).
- Then use $S = \frac{n}{2}(a + l)$ — the shorter sum formula when both first and last terms are known. This saves calculation time.
- Both steps are needed for full 2 marks; losing either costs 1 mark.