SOLUTION: In a certain geometric sequence, t sub3 = 400 and t sub5 = 25. What could the value of t sub8 be?

Question 1112832: In a certain geometric sequence, t sub3 = 400 and t sub5 = 25. What could the value of t sub8 be?
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If the common ratio is , and the th term is and the th term is , then

Hence

Then

and

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The answer from the other tutor is only half right.

Since the ratio of t3 to t5 is 1/16, the common ratio in the geometric sequence could be either 1/4 or -1/4. So 25/64 is one possible value for t8; the other is -25/64.
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