SOLUTION: 1) A second term of a geometric sequence is 24, the fifth term is 81. find the 7th term. 2) find the 5th term of sequence -3,2,7.......

Algebra ->  Sequences-and-series -> SOLUTION: 1) A second term of a geometric sequence is 24, the fifth term is 81. find the 7th term. 2) find the 5th term of sequence -3,2,7.......      Log On


   

Question 1056796: 1) A second term of a geometric sequence is 24, the fifth term is 81. find the 7th term.
2) find the 5th term of sequence -3,2,7.......
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
General term is A%2Ar%5E%28n-1%29.
system%28A%2Ar%5E%282-1%29=24%2CA%2Ar%5E%285-1%29=81%29
-
system%28Ar=24%2CAr%5E4=81%29

%28Ar%5E4%29%2F%28Ar%29=81%2F24

r%5E3=%289%2A9%29%2F%283%2A2%2A2%2A2%29

r%5E3=27%2F%282%2A2%2A2%29

r%5E3=%283%5E3%29%2F%282%5E3%29

r=3%2F2

General Term more specifically is A%283%2F2%29%5E%28n-1%29. You still need to know A, before you can find the term for any index n.

A%283%2F2%29=24
A=24%282%2F3%29
A=16 and from this you know the general term is highlight%2816%283%2F2%29%5E%28n-1%29%29.