SOLUTION: Find a_5 for the following geometric sequence: a_2=4096, r=1/4? Thank you.

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Question 986853: Find a_5 for the following geometric sequence: a_2=4096, r=1/4?
Thank you.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find a%5B5%5D for the following geometric sequence: a%5B2%5D = 4096, r = 1/4.
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a%5B3%5D = 4096.1%2F4 = 1024,

a%5B4%5D = 1024.1%2F4 = 256,

a%5B5%5D = 256.1%2F4 = 64.

Answer.  a%5B5%5D = 64.


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Find a_5 for the following geometric sequence: a_2=4096, r=1/4?
Thank you.
Formula for a term in a geometric sequence: a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29
We then get: a%5B2%5D+=+a%5B1%5D+%2A+%281%2F4%29%5E%282+-+1%29
4096+=+a%5B1%5D+%2A+%281%2F4%29
a%5B1%5D+=+4096%2F%281%2F4%29
a%5B1%5D+=+4096+%2A+4%29
a%5B1%5D+=+16384

a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29
We then get: a%5B5%5D+=+16384+%2A+%281%2F4%29%5E%285+-+1%29
a%5B5%5D+=+16384+%2A+%281%2F4%29%5E4
a%5B5%5D+=+16384+%2A+%281%2F4%5E4%29
a%5B5%5D+=+16384+%2A+%281%2F256%29
a%5B5%5D+=+64cross%2816384%29+%2A+%281%2Fcross%28256%29%29
highlight_green%28a%5B5%5D+=+64%29