Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 4

True

Write the sum $S_n$ of the first $n$ terms of an arithmetic sequence in two ways: $S_n=a_1+a_2+a_3+.........+a_{n-1}+a_n$ $S_n=a_n+a_{n-1}+.............+a_2+a_1$ Add the equations side by side: $2S_n=(a_1+a_n)+(a_2+a_{n-1})+.....+(a_n+a_1)$ As $a_1+a_n=a_2+a_{n-1}=.......=a_n+a_1$, we have: $2S_n=n(a_1+a_n)$ $S_n=\dfrac{n(a_1+a_n)}{2}$ Therefore the statement is TRUE.