SOLUTION: Find the general rule of the following sequence. Show your solution 1/2,2,27/8,4,...

Question 1183824: Find the general rule of the following sequence. Show your solution
1/2,2,27/8,4,...

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

1/2, 2, 27/8, 4, ...

Given that the 1st and 3rd terms are fractions but the others are not, rewrite the sequence as all fractions, using denominators that form a recognizable pattern.

The denominator of the 1st term is 2; the denominator of the 3rd term is 8. So one "nice" pattern for the denominators would be 2, 4, 8, 16, .... Using those denominators, the sequence is

1/2, 8/4, 27/8, 64/16, ...

The numerators are now 1, 8, 27, 64, ..., which are 1^3, 2^3, 3^3, and 4^3. So the pattern for the sequence appears to be

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