Find the sum of the first 12 terms of an arithmetic progression with first term 15 and common difference $-3$.

Step-by-step solution

1. Apply the sum formula $S_n=\frac{n}{2}[2a+(n-1)d]$.
2. Here $n=12$, $a=15$, $d=-3$.
3. Compute the bracket: $2a+(n-1)d=2\times 15+11\times (-3)=30-33=-3$.
4. Now $S_{12}=\frac{12}{2}\times (-3)=6\times (-3)=-18$.
5. Hence the required sum is $-18$.

Concept tested: sum of n terms of AP

Published 28 September 2026 · How this solution was prepared and checked

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