Question

HELP ASAP !!!What is the sum of the geometric series

Answer 1

see explanation

Explanation:

The ones ticked are correct

Given

6 + 18 + 54 + 162 + 486

There is a common ratio r between consecutive terms, that is

18 ÷ 6 = 54 ÷ 18 = 162 ÷ 54 = 486 ÷ 162 = 3

This indicates the series is geometric with explicit formula

`a_(k)` = a
`(r)^(k-1)`

where a is the first term and r the common ratio

Here a = 6 and r = 3, thus explicit formula is

`a_(k)` = 6
`(3)^(k-1)`

The series in summation form with 5 terms in the series is

∑ 6
`(3)^(k-1)` for k = 1 to 5

Sum = 6 + 18 + 54 + 162 + 486 = 726