What is the sum of the first $5$ terms of the arithmetic progression with first term $3$ and common difference $4$?

Step-by-step solution

1. Recall the sum formula: $S_n=\frac{n}{2}[2a+(n-1)d]$.
2. Substitute $n=5$, $a=3$, $d=4$: $S_5=\frac{5}{2}[2\times 3+(5-1)\times 4]$.
3. Simplify inside the brackets: $2\times 3=6$ and $(5-1)\times 4=16$, so $6+16=22$.
4. Compute the product: $\frac{5}{2}\times 22=\frac{5\times 22}{2}=\frac{110}{2}=55$.
5. Hence the correct option is A. 55.

Concept tested: sum of n terms of AP

Published 21 August 2026 · How this solution was prepared and checked

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