Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Quiz for Lessons 12.1-12.3 - Page 817: 10

$a_n=6n-5$ and $S_{15}=645$

The nth term is given by $a_n= a_1+(n-1) d$ ...(1) Here, we have Common Difference $d=6$ and first term $a_1=1$ Equation (1) gives: $a_n=1+6(n-1)=6n-5$ Plugging in $n =15$, we have $a_{15}=6 (15)-5=85$ We know that $S_{n}=\dfrac{n(a_1+a_{15})}{2}$ Now, $S_{15}=\dfrac{15 (1+85)}{2}=645$