An arithmetic sequence has first term $a_{1} = 3$ and common difference $d = 6$. What is the $15$th term?

Use the explicit formula for an arithmetic sequence: $a_{n} = a_{1} + (n - 1) d$. With $a_{1} = 3$, $d = 6$, $n = 15$: $a_{15} = 3 + (15 - 1)(6) = 3 + 14 \times 6 = 3 + 84 = 87$. - Trap A ($84$) stops at $(n-1)d$ without adding $a_{1}$. - Trap C ($90 = 15 \times 6$) uses $nd$ instead of $a_{1} + (n-1)d$ — forgetting both the $-1$ and the constant term. - Trap D is the result of using $n = 16$ accidentally. The sequence runs $3, 9, 15, 21, \ldots$ — each term $6$ more than the last. After $14$ steps from the first term, we land on the $15$th.