What is the sum of the first $30$ terms of the arithmetic sequence $8, 13, 18, 23, 28, \ldots$?

Identify the sequence parameters: $a_{1} = 8$, common difference $d = 5$. Find the $30$th term: $a_{30} = a_{1} + (n - 1)d = 8 + 29 \times 5 = 8 + 145 = 153$. Apply the sum formula: $S_{n} = \dfrac{n}{2}(a_{1} + a_{n})$: $S_{30} = \dfrac{30}{2}(8 + 153) = 15 \times 161 = 2{,}415$. - Trap D ($4{,}830 = 30 \times 161$) forgets the factor of $1/2$. - Trap B is roughly $S_{n}$ computed with the wrong last term. Mnemonic for arithmetic sums: $S_{n}$ equals the number of terms times the **average** of the first and last, since the terms are evenly spaced. The average of $8$ and $153$ is $80.5$, and $30 \times 80.5 = 2{,}415$ ✓.