Question

Find the sum of the n terms using the formula a(1-r^n)/1-r 1,3/2,9/4,27/8,81/16, …

Answer 1

`S_5=(211)/(16)`

Explanation:

We can easily see that the common ratio is
`r=(3)/(2)` and we are to find the first
`n=5` terms:

`\displaystyle S_n=(a_1(1-r^n))/(1-r)\\\\S_5=(1(1-((3)/(2))^5))/(1-(3)/(2))\\\\S_5=(1-(243)/(32))/(-(1)/(2))\\ \\S_5=(-(211)/(32))/(-(1)/(2))\\ \\S_5=(422)/(32)\\\\S_5=(211)/(16)`