Chapter 14 - Sequences, Series, and the Binomial Theorem - Mid-Chapter Review - Mixed Review - Page 915: 5

$S_{12}=78$

We need to find the sum of the first $12$ terms $S_{12}$ of the sequence $1, 2 ,3 ,4, . . ., n, . . .$ This is the simplest arithmetic progression with the general term $a_n=n$. The sum of the first $n$ terms is $S_{n}=\dfrac{a_1+a_n}{2}n$ We substitute $a_1=1$, $n=12$ and $a_n=a_{12}=12$, so we have: $S_{12}=\frac{1+12}{2}\cdot 12=\frac{13}{2}\cdot 12=13\cdot6=78$