Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Skill Practice - Page 807: 60

$n=9$

For an arithmetic series, the sum for the finite series is given by: $S_n=\dfrac{n(a_1+a_n)}{2}$ The sum of the first four terms is: $S_n=\dfrac{4(19+55)}{2}=148$ and $a_n=7+12n$ $S_n=455+148=\dfrac{n \times (19+(7+12n))}{2}$ or, $6n^2+13n-603=0$ or, $(n-9) (6n+67)=0$ This gives: $n=\dfrac{-67}{6}; 9$ Hence, the positive solution for $n$ is $n=9$.