SOLUTION: given a term in a geometric sequence and the common ratio find the term named in the problem and the explicit formula http://prntscr.com/s9icar

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Question 1157838: given a term in a geometric sequence and the common ratio find the term named in the problem and the explicit formula
http://prntscr.com/s9icar
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
#19:
system%28a%5B6%5D=-128%2Cr=-2%29

General term, %28-2%29%2A2%5En


What will be sixth term, or at index 6?
1        4
2         -8
3        16
4        -32
5        64
6      -128

If you then want term at index 11, just substitute 11 for the general term formula.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
given a term in a geometric sequence and the common ratio find the term named in the problem and the explicit formula
http://prntscr.com/s9icar
Term of a G.P. formula: matrix%281%2C3%2C+a%5Bn%5D%2C+%22=%22%2C+a%5B1%5Dr%5E%28n+-+1%29%29

matrix%281%2C3%2C+a%5B6%5D%2C+%22=%22%2C+a%5B1%5D%28-+2%29%5E%286+-+1%29%29 ----- Substituting 6 for n, and - 2 for r

matrix%281%2C3%2C+-+128%2C+%22=%22%2C+a%5B1%5D%28-+2%29%5E5%29 ------ Substituting matrix%281%2C3%2C+-++128%2C+for%2C+a%5Bn%5D%29

matrix%281%2C3%2C+-+128%2C+%22=%22%2C+a%5B1%5D%28-+32%29%29

matrix%281%2C3%2C+%28-+128%29%2F%28-+32%29%2C+%22=%22%2C+a%5B1%5D%29

matrix%281%2C3%2C+4%2C+%22=%22%2C+a%5B1%5D%29 

For the value of a%5B11%5D, or the 11th term, substitute matrix%283%2C3%2C+11%2C+for%2C+n%2C+4%2C+for%2C++a%5B1%5D%2C+-+2%2C+for%2C+r%29 into the G.P. formula: matrix%281%2C3%2C+a%5Bn%5D%2C+%22=%22%2C+a%5B1%5Dr%5E%28n+-+1%29%29, and SIMPLIFY.