Chapter 9 - Conic Sections, Sequences, and Series - 9.5 Series - 9.5 Exercises - Page 747: 27

$3629.6$

$a_{n+1}-a_n=2.4(n+1)+6.2-(2.4n+6.2)=2.4$ Since the difference between consecutive terms is constant, the given sequence is arithmetic. The formula for the finite sum of the arithmetic sequence is: $S_{n}=\frac{n(a_{1}+a_{n})}{2}$ $a_{n}=2.4n+6.2$ $a_{1}=2.4(1)+6.2=8.6$ . $a_{52}=2.4(52)+6.2=131$ $S_{52}=\frac{52(a_{1}+a_{52})}{2}=\frac{52(8.6+131)}{2}=3629.6$