SOLUTION: The third term of a geometric sequence is 12 and the fifth term is 16/3. Determine the formula for a⬇️n, nth term of this sequence. Find the value of a⬇️25. (25 is bene

Algebra ->  Test -> SOLUTION: The third term of a geometric sequence is 12 and the fifth term is 16/3. Determine the formula for a⬇️n, nth term of this sequence. Find the value of a⬇️25. (25 is bene      Log On


   

Question 1154630: The third term of a geometric sequence is 12 and
the fifth term is 16/3.
Determine the formula for a⬇️n, nth term of this sequence.
Find the value of a⬇️25. (25 is beneath a and n is beneath a as well)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The 5th term is the 3rd term, multiplied by the common ratio 2 times:

16%2F3+=+12%28r%5E2%29
r%5E2+=+%2816%2F3%29%2F12+=+16%2F36+=+4%2F9
r+=+2%2F3 OR r+-2%2F3

We can write a formula for the nth term of the sequence using any known term; it is not necessary to find the first term. I will use the given 3rd term.

Since there are two possible values for the common ratio, there are different possible formulas for the n-th term.

t%28n%29+=+12%28%282%2F3%29%5E%28n-3%29%29 OR t%28n%29+=+12%28%28-2%2F3%29%5E%28n-3%29%29

The 25th term will be the same using either formula, because the exponent will be even.

t%2825%29+=+12%28%282%2F3%29%5E22%29

Use a calculator....