Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 55

$12$

For an arithmetic series, the sum for the finite series is given by: $S_n=\dfrac{n(a_1+a_n)}{2}$ We are given that $S_n=486$ Now, $486=\dfrac{n \times (2+[-5+7n])}{2}$ or, $-3n+7n^2=972$ or, $7n^2-3n-972=0$ or, $(n-12) (7n+81)=0$ This gives: $n=12,-81/7$ Hence, the positive solution for $n$ is $n=12$