Question 978613: Given the geometric sequence: 20,(5/2),(5/16) ...
Find an explicit formula for a_n.
a_n =
Find a_(8) =
Found 2 solutions by Boreal, Cromlix:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the ratio is from 20 to 5/2 or from 40/2 to 5/2 and that is 1/8.
A(n)=A*r^n-1
n=8
n-1=7
A=20
r=1/8
EXPLICIT FORMULA IS A(n)=20*(1/8)^n-1
A(8)=20*(1/8)^7
=9.536 X 10^-6, or 0.000009536
For a fraction,
5 will be the numerator, and 16*(8^5), which are the number of terms left for the denominator,=
524288
5/(524288)=the above number.
Answer by Cromlix(4381)  (Show Source):
You can put this solution on YOUR website! Hi there,
20,(5/2),(5/16) ...
Find 'r' Using 1st and 2nd numbers
5/2 / 20 = 5/40 = 1/8
An = 20* (1/8)^n-1
A(8) = 20*(1/8)^7
A^8 = 5/524288
Hope this helps:-)
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