Arithmetic Series Formula

The sum of an arithmetic sequence with $n$ terms, first term $a_1$, and last term $a_n$ is: $S = \frac{n(a_1 + a_n)}{2}$.

This formula says: multiply the number of terms by the average of first and last, then divide by two. It generalizes the $1 + 2 + ... + n$ formula.

For the sequence $5, 8, 11, 14, 17$ (5 terms), the sum is $\frac{5(5 + 17)}{2} = \frac{5 \times 22}{2} = 55$. Check: $5 + 8 + 11 + 14 + 17 = 55$.