Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Quiz for Lessons 12.1-12.3 - Page 817: 12

$a_n=8-3n$ $a_{15}=-37$ $S_{15}=-240$

The nth term is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have Common Difference $d=3$ and first term $a_1=5$ Equation (1) gives: $a_n=5+3 \times (n-1)=8-3n$ Plugging in $n =15$, we have $a_{15}=8-3(15)=-37$ We know that $S_{n}=\dfrac{n(a_1+a_{15})}{2}$ Now, $S_{15}=\dfrac{15 (5+(-37)}{2}=-240$