Question

9.1.3 Quiz: Geometric Sequences
Question 6 of 10
2 Points
What is the sum of the first five terms of a geometric series with an = 6 and
r=1/3?
Express your answer as an improper fraction in lowest terms without using
spaces.
Answer here

Answer 1

Your geometric series starts with 6, and then you get the next term by multiplying the previous one by 1/3. So, the first five terms are

$a_1=6$

$a_2=6\cdot\dfrac{1}{3}=2$

$a_3=2\cdot\dfrac{1}{3}=\dfrac{2}{3}$

$a_4=\dfrac{2}{3}\cdot\dfrac{1}{3}=\dfrac{2}{9}$

$a_5=\dfrac{2}{9}\cdot\dfrac{1}{3}=\dfrac{2}{27}$

And if we sum them we have

$8+\dfrac{2}{3}+\dfrac{2}{9}+\dfrac{2}{27}=\dfrac{242}{27}$