Question

2. Find the sum of the first 6 terms of the geometric series.

3+15+75+375+....
(Use the formula Sn = 41(1r") to find Sø)
1-r

Answer 1

(a)
`S_6=1092`

(b)
`S_5=363`

Explanation:

Question 1

Given the geometric series

3+15+75+375+...

`a_1=3, r=15/3=75/15=5\\$Therefore using:\\S_n=(a_1(1-r^n))/(1-r) \\S_6=(3(1-3^6))/(1-3)=(3(-728))/(-2)=(-2184)/(-2)\\\\S_6=1092`

Question 2

Given the series:
`\sum_(n=1)^5 3^n`

`3^1=3;3^2=9;3^3=27\\$The series is 3+9+27+\cdots\\$Therefore: r=9/3=27/9=3`

`a_1=3, r=3\\$Therefore using:\\S_n=(a_1(1-r^n))/(1-r) \\S_5=(3(1-3^5))/(1-3)=(3(-242))/(-2)=(-726)/(-2)\\\\S_5=363`