Question

Plzz someone help!!! i will mark barinliest!!!worth 20 points!

Answer 1

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

$a, ar, ar^{2}, ar^{3}, ar^{4}, ...$

where a denotes the intial term and r denotes the common ratio.

The nth term of the series can be found by the formula

$a_{n}=ar^{n-1}$

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,

$a_{20}=ar^{20-1}=(6)(3^{19})\\\\=(6)(1162261467)=6973568802$

Thus, Kendall will do 6973568802 pushups in the 20th week.

Answer 2

Answer:

a: 3

b: 183514968.4

Step-by-step explanation:

find the geometric sequence and plug it in