SOLUTION: For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to −44. Find the value of the 12th term, a12. If applicable, write your

Algebra ->  Sequences-and-series -> SOLUTION: For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to −44. Find the value of the 12th term, a12. If applicable, write your      Log On


   

Question 1038972: For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to −44. Find the value of the 12th term, a12. If applicable, write your answer as a fraction.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to 44.
Find the value of the 12th term, a12. If applicable, write your answer as a fraction.
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Take the ratio a%5B10%5D%2Fa%5B5%5D = 44%2F%28%2811%2F256%29%29 = 256%2A4 = 1024 = 2%5E10.

Take the 5-degree root of this ratio: root%285%2C+2%5E10%29 = 2%5E2 = 4.

It is your r, the common ratio.

Then multiply a%5B10%5D by r%5E2.

You will get 44%2A4%5E2 = 704.

It is your answer.

As the last step, think, why it is correct.

Your lesson on geometric progressions is Geometric progressions in this site.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to −44. Find the value of the 12th term, a12. If applicable, write your answer as a fraction. 
Common ratio: - 4

12th term, or