Answer:
see explanation
Step-by-step 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
[tex]a_{k}[/tex] = a [tex](r)^{k-1}[/tex]
where a is the first term and r the common ratio
Here a = 6 and r = 3, thus explicit formula is
[tex]a_{k}[/tex] = 6 [tex](3)^{k-1}[/tex]
The series in summation form with 5 terms in the series is
∑ 6 [tex](3)^{k-1}[/tex] for k = 1 to 5
Sum = 6 + 18 + 54 + 162 + 486 = 726
