Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - 12.1 Exercises - Skill Practice - Page 798: 41

$\displaystyle \sum_{n=1}^{\infty}(7n-4)$

Note the common difference between terms $a_{1}=3$ $a_{2}=10=a_{1}+7$ $a_{3}=17=a_{2}+7=a_{1}+2(7)$ $a_{4}=24=a_{3}+7=a_{1}+3(7)$ $a_{5}=31=a_{4}+7=a_{1}+4(7)$ $...$ $a_{n}=3+7(n-1)=3+7n-7=7n-4,$ Beginning with n=1 (lower limit) and never ending (no upper limit) Sum = $\displaystyle \sum_{n=1}^{\infty}(7n-4)$