Given:
The sequence 6, 18, 54, 162, …
To Find:
- The common ratio in this sequence
- and the number of pushups Kendall will do on the 20th week.
Answer:
Kendall will do 6973568802 pushups in the 20th week.
Step-by-step explanation:
The given sequence 6, 18, 54, 162, ... is a geometric series.
A geometric series is a sequence of numbers where each succeeding term can be found by multiplying the previous term with a constant factor which is called the common ratio.
We see that in the given sequence, each successive term can be found by multiplying the previous term by 3.
18 = 6 multiplied by 3
54 = 18 multiplied by 3
162 = 54 multiplied by 3
and so on.
So, the common ratio is 3.
The general form of a geometric series can be written as
[tex]a, ar, ar^{2}, ar^{3}, ar^{4}, ...[/tex]
where a denotes the intial term and r denotes the common ratio.
The nth term of the series can be found by the formula
[tex]a_{n}=ar^{n-1}[/tex]
For the given sequence, intial term a = 6 and common ratio r = 3.
To find the number of pushups Kendall will do on the 20th week, we need to calculate the 20th term.
That is,
[tex]a_{20}=ar^{20-1}=(6)(3^{19})\\\\=(6)(1162261467)=6973568802[/tex]
Thus, Kendall will do 6973568802 pushups in the 20th week.
