Question

Identify the 16th term of a geometric sequence where a1 = 4 and a8 = −8,748... How do I find the value of r????

Answer 1

r = -3

16th term: -516560652

Explanation:

Let's use the formula for a geometric sequence:

, where is the nth term, is the first term, and r is the common ratio

Here, we know the first term is 4. To find r, let's plug in 8 for n and -8748 for :

-8748 = 4 *

-8748 = 4 *

= -2187

r = -3

Answer 2

r = -3

16th term: -516560652

Explanation:

Let's use the formula for a geometric sequence:

`a_n=a_1r^(n-1)`, where
`a_n` is the nth term,
`a_1` is the first term, and r is the common ratio

Here, we know the first term is 4. To find r, let's plug in 8 for n and -8748 for
`a_n`:

`a_n=a_1r^(n-1)`

-8748 = 4 *
`r^(8-1)`

-8748 = 4 *
`r^7`

`r^7` = -2187

r = -3

So we know that the common ratio is -3. Now, we want to find the 16th term, so n = 16:

`a_n=a_1r^(n-1)`

`a_(16)=a_1*(-3)^(16-1)=4*(-3)^(17)=-516560652`