Question 1183824
<br>
1/2, 2, 27/8, 4, ...<br>
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.<br>
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<br>
1/2, 8/4, 27/8, 64/16, ...<br>
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<br>
{{{t(n) = n^3/2^n}}}<br>