Question

A geometric sequence has a first term of 3 and a fourth term of 81/8
Find the eighth term.

Answer 1

Answer:

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The second term is 3 and the fifth term is 81/8 (or 10.125)

Let the growth at each step equal xx.

This means that over three geometric steps, the total growth is x3x3.

So:

x3=10.125/3x3=10.125/3

x3=3.375x3=3.375

x=1.5x=1.5

To get the fourth term, let’s just multiply 2 by xx twice, so:

3∗x∗x=3∗1.5∗1.5=6.753∗x∗x=3∗1.5∗1.5=6.75

So the answer is 6.75.