Question 931507: 1/3, 8/3, 27/3, 64/3, 125/3 identify the sequence
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is:
An = A1 * n^3
A1 = 1/3 * 1^3 = 1/3 * 1 = 1/3
A2 = 1/3 * 2^3 = 1/3 * 8 = 8/3
A3 = 1/3 * 3^3 = 1/3 * 27 = 27/3
A4 = 1/3 * 4^3 = 1/3 * 64 = 64/3
A5 = 1/3 * 5^3 = 1/3 * 125 = 125/3
this is a geometric type sequence with a common ratio of n^3.
this is not a pure geometric sequence because the ratio changes each time.
in a pure geometric sequence the ratio remains the same.
an example of that would be An = 1/3 * 2^(n-1), where the common ratio is 2 and will always be 2.
with this sequence, you get An = A1 * n^3 where the common ratio is n^3 that keeps changing as you go from one n to another. when n = 2, the common ratio is 2^3, when n = 3, the common ratio is 3^3, etc. the only common thing about it is that n is constantly being cubed.
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