SOLUTION: what is the general term or nth term of the sequence 1/4,9/16,81/64,729/256,...? A. 9^n-1/4^n+1 B. 9^n-1/4^n C. 9^n/4^n-1 D. 9^n+1/4^n

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is the general term or nth term of the sequence 1/4,9/16,81/64,729/256,...? A. 9^n-1/4^n+1 B. 9^n-1/4^n C. 9^n/4^n-1 D. 9^n+1/4^n      Log On


   

Question 1172497: what is the general term or nth term of the sequence 1/4,9/16,81/64,729/256,...?
A. 9^n-1/4^n+1
B. 9^n-1/4^n
C. 9^n/4^n-1
D. 9^n+1/4^n
Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

The 1st term, index n=1, (a%5B1%5D) is 9%5E0+%2F+4%5E1+ = +9%5E%281-1%29+%2F+4%5E1
For n=2, you have +9%5E%282-1%29+%2F+4%5E2+ ...


You should see the pattern now...

B

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


The ratio of the second term to the first term is %289%2F16%29%2F%281%2F4%29+=+%289%2F4%29.

The ratio of the third term to the second term is %2881%2F64%29%2F%289%2F16%29+=+%289%2F4%29.

The ratio of the fourth term to the third term is %28729%2F256%29%2F%2881%2F64%29+=+%289%2F4%29.

The sequence is geometric, with first term 1/4 and common ratio 9/4:

t%28n%29+=+%281%2F4%29%289%2F4%29%5E%28n-1%29

That is equivalent to t%28n%29+=+9%5E%28n-1%29%2F4%5En, or 9^(n-1)/4^n.

Technically, none of the given answer choices is correct, because they are all written incorrectly; required parentheses are missing.

Answer B is supposed to be the right answer; but as it is written that answer is 9^n-1/4^n = 9%5En-1%2F4%5En

That is clearly something very different from the correct expression.