Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 815: 60

13 terms or 27 terms

We are given the arithmetic sequence: $a_1=78$ $d=-4$ $S_n=702$ We determine $n$ solving the equation: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $702=\dfrac{n(2(78)+(n-1)(-4))}{2}$ $2(702)=n(156-4n+4)$ $1404=-4n^2+160n$ $4n^2-160n+1404=0$ $4(n^2-40n+351)=0$ $n^2-40n+351=0$ $n=\dfrac{40\pm\sqrt{(-40)^2-4(1)(351)}}{2(1)}=\dfrac{40\pm 14}{2}=20\pm 7$ $n_1=20-7=13$ $n_2=20+7=27$ Both solutions fit.