SOLUTION: write a formula for then term of the sequences 0 3 8 15 24 35 1 1/2 1/4 1/8 1/16.....

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Question 957478: write a formula for then term of the sequences 0 3 8 15 24 35
1 1/2 1/4 1/8 1/16.....
Found 2 solutions by KMST, stanbon:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The term number n for 0 3 8 15 24 35 is
T%5Bn%5D=n%5E2-1 :
T%5B1%5D=1%5E2-1=1-1=0 ,
T%5B2%5D=2%5E2-1=4-1=3 ,
T%5B3%5D=3%5E2-1=9-1=8 ,
T%5B4%5D=4%5E2-1=16-1=15 ,
and so on,
The term number n for 1 1/2 1/4 1/8 1/16..... is
T%5Bn%5D=1%2F%282%5E%28n-1%29%29 , or T%5Bn%5D=%281%2F2%29%5E%28n-1%29 :
T%5B1%5D=1%2F%282%5E%281-1%29%29=1%2F%282%5E0%29=1%2F1=1 ,
T%5B2%5D=1%2F2%5E1=1%2F2 ,
T%5B3%5D=1%2F2%5E2=1%2F4 ,
T%5B4%5D=1%2F2%5E3=1%2F8 , and so on.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write a formula for then term of the sequences
0 3 8 15 24 35
-----
a(1) = 0
a(2) = 3 = 2*2-1
a(3) = 8 = 2*3-1
a(4) = 15 = 2*8 - 1
a(n+1) = 2*n - 1
------------------------------------
1 1/2 1/4 1/8 1/16.....
---
a(n) = 1/n^2
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Cheers,
Stan H.
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