Chapter 11 - Section 11.2 - Arithmetic Sequences - Exercise Set - Page 842: 87

$200^{th}$ term

An arithmetic sequence is defined as a sequence which has a common difference $d$ and calculated as: $a_n=a_1+(n-1)d$ Need to calculate $n$. Thus, $a_n=a_1+(n-1)d$ $\implies 314628=21700+1472(n-1)$ $\implies 314628=20228+1472n$ or, $n=200$, that is, $200^{th}$ term