SOLUTION: find the value of x in the sequence 1/2, x, 1/8 if the sequence4 is an arithmetic progression and a geometric progression

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Question 757444: find the value of x in the sequence 1/2, x, 1/8 if the sequence4 is an arithmetic progression and a geometric progression
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
find the value of x in the sequence 1/2, x, 1/8 if the sequence is an arithmetic progression and a geometric progression
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A:
If the sequence is an arithmetic progression,then
x - 1/2 = 1/8 - x
x + x = 1/8 + 1/2
2x = 5/8
x = highlight%285%2F16%29
If the sequence is a geometric progression, then
x%2F%281%2F2%29 = %281%2F8%29%2Fx
x%5E2 = 1%2F16
x = ±sqrt%281%2F16%29
= highlight%281%2F4%29 OR highlight%28-1%2F4%29