Question

What is the 8th term of the sequence? −16, 24, −36, 54, ... −729/8 2187/8 −2187/8 729/8

Answer 1

Answer:

The answer is

$\frac{2187}{8}$

Step-by-step explanation:

The sequence above is a geometric sequence

For an nth term in a geometric sequence

$A(n) = a ({r})^{n - 1}$

where n is the number of terms

r is the common ratio

a is the first term

From the question

a = - 16

To find the common ratio divide the previous term by the next term

That's

r = 24/-16 = -3/2 or -36/24 = - 3/2

Since we are finding the 8th term

n = 8

Substitute the values into the above formula

That's

$A(8) = - 16 ({ - \frac{3}{2} })^{8 - 1}$

$A(8) = - 16 ({ - \frac{3}{2} })^{7}$

$A(8) = - 16( - \frac{2187}{128} )$

We have the final answer as

$A(8) = \frac{2187}{8}$

Hope this helps you