SOLUTION: Find the nth term of the geometric sequence 125,25,5,1... Find the nth term of the geometric sequence 7,49,343,2401,...

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Question 659640: Find the nth term of the geometric sequence
125,25,5,1...
Find the nth term of the geometric sequence
7,49,343,2401,...

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the nth term of the geometric sequence
125,25,5,1...
a(n) = 125(1/5)^(n-1)
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Find the nth term of the geometric sequence
7,49,343,2401,...
a(n) = 7^n
===================
Cheers,
Stan H.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the nth term of the geometric sequence
125,25,5,1...1%2F5,1%2F25...every next one is divided by 5, so ratio is 1%2F5
nth of General Term of a Geometric Sequence: a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29+

where a%5B1%5D is the first term of the sequence and r is the common ratio.
We have the common ratio r=1%2F5 and a%5B1%5D=125,then
highlight%28a%5Bn%5D=125%2A%281%2F5%29%5E%28n-1%29%29+

so, check sixth term above using this formula:
a%5B6%5D=125%2A%281%2F5%29%5E%286-1%29+
a%5B6%5D=125%2A%281%2F5%29%5E5+

a%5B6%5D=125%2A%281%2F25%29=0.04+ which is 1%2F25


Find the nth term of the geometric sequence
7,49,343,2401,...
it is a "geometric sequence" which that means that each successive term is multiplied by the same factor, and in this sequence the common factor is f=7
Geometric sequences have an nth term of the form a%5Bn%5D=+a%5B1%5Df%5E%28n-1%29+ where a%5B1%5D is the first term, f is the common factor and n is the number of the term (nth term).
highlight%28a%5Bn%5D=+a%5B1%5D7%5E%28n-1%29%29+ .......a%5B1%5D=7 and f=7