SOLUTION: The second and fifth terms of a geometric progressions are 16 and 2 respectively. Determine the common ratio and the first term

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Question 1155543: The second and fifth terms of a geometric progressions are 16 and 2 respectively. Determine the common ratio and the first term
Answer by math_helper(2461) About Me  (Show Source):
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The general form is a, ak, ak^2, ak^3, ... etc.
Where a=first term (often used with subscripts a%5B1%5D)
k=common ratio
Given info:
+k%2Aa%5B1%5D+=+16+
+k%5E4%2Aa%5B1%5D+=+2+
Notice that +%28k%5E4%2Aa%5B1%5D%29%2F%28k%2Aa%5B1%5D%29+=+k%5E3+=+2%2F16+=+1%2F8+
so +k+=+root%283%2C%281%2F8%29%29+=+1%2F2+
Common ratio: +highlight%281%2F2%29+
The first term can be found by dividing k*a by k: 16/(1/2) = 32
First term: +highlight%28a%5B1%5D+=+32+%29+