### Home > PC > Chapter 7 > Lesson 7.3.2 > Problem7-108

7-108.

A series has four terms, starts with $5$, and has a sum of $200$.

1. What are the terms if the series is arithmetic?

$S=\frac{n(a_{1}+a_{n})}{2}$

$200=\frac{4(5+a_{n})}{2}$

$400 = 20 + 40a_{n}$

$380 = 40a_{n}$

$95 = a_{n}$

$\frac{95-5}{3}=30$

Series $= 5 + 35 + 65 + 95$

2. What are the terms if the series is geometric?

$S=\frac{a(r^{n}-1)}{r-1}$

$200=\frac{5(r^{4}-1)}{r-1}$

$200=\frac{5(r-1)(r+1)(r^{2}+1)}{r-1}$

$200 = 5\left(r + 1\right)\left(r^{2} + 1\right)$

By inspection $= 3$.

Series $= 5 + 15 + 45 + 135$