Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 56

$-3013$

We are given the sequence: $2,-1,-4,-7,......$ As $-1-2=-4-(-1)=-7-(-4)=-3$, the sequence is arithmetic. Determine its first term and common difference: $a_1=2$ $d=-3$ We determine the sum of the first 46 terms using the formula: $S_n=\dfrac{n(2a_1+(n-1)d}{2}$ $S_{46}=\dfrac{46(2\cdot 2+(46-1)\cdot (-3))}{2}=\dfrac{46(-131)}{2}=-3013$