Question 1172497
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The ratio of the second term to the first term is {{{(9/16)/(1/4) = (9/4)}}}.<br>
The ratio of the third term to the second term is {{{(81/64)/(9/16) = (9/4)}}}.<br>
The ratio of the fourth term to the third term is {{{(729/256)/(81/64) = (9/4)}}}.<br>
The sequence is geometric, with first term 1/4 and common ratio 9/4:<br>
{{{t(n) = (1/4)(9/4)^(n-1)}}}<br>
That is equivalent to {{{t(n) = 9^(n-1)/4^n}}}, or 9^(n-1)/4^n.<br>
Technically, none of the given answer choices is correct, because they are all written incorrectly; required parentheses are missing.<br>
Answer B is supposed to be the right answer; but as it is written that answer is 9^n-1/4^n = {{{9^n-1/4^n}}}<br>
That is clearly something very different from the correct expression.<br>