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

1 Answer

7 votes

Answer:

The answer is


(2187)/(8)

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 ({ - (3)/(2) })^(8 - 1)


A(8) = - 16 ({ - (3)/(2) })^(7)


A(8) = - 16( - (2187)/(128) )

We have the final answer as


A(8) = (2187)/(8)

Hope this helps you

User Johneric
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