SOLUTION: A geometric sequence in which the third term is 4 and the sixth term is 256. Write this sequence.

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Question 934972: A geometric sequence in which the third term is 4 and the sixth term is 256. Write this sequence.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
4=2%5E2, 256=2%5E8.


a%5B3%5D,a%5B3%5D%2Ar,a%5B3%5D%2Ar%5E2,a%5B4%5D%2Ar%5E3

Sixth term is 4%2Ar%5E3=256
r%5E3=64
r%5E3=%282%5E3%29%5E2
r%5E3=2%5E6
highlight_green%28r=4%29.

Work backward using that common ratio from term at index 3 to term at index 1.
4%2F4=1;
1%2F4=1%2F4------------the term, a%5B1%5D.

General term for the sequence is highlight%28%281%2F4%29%5E%28n-1%29%29.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

A geometric sequence in which the third term is 4 and the sixth term is 256. Write this sequence.


highlight_green%28a%5Bn%5D+=+%281%2F4%29%284%29%5E%28n+-+1%29%29