SOLUTION: determine the common ratio of a geometric sequence whose first term is 2 and whose fourth term is 16?

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Question 126680: determine the common ratio of a geometric sequence whose first term is 2 and whose fourth term is 16?
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
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Question:
determine the common ratio of a geometric sequence whose first term is 2 and whose fourth term is 16?

Answer,
The nth term of a geometric series is given by the formula,
n th term = +a%28r%29%5E%28n-1%29, where r is the common ratio and a is the first term.

So, fourth term = +a%28r%29%5E3

here first term is given as 2and fourth term is 16.

so, 16 = +2%28r%29%5E3

divide both sides by 2

==> 16/3 = +%282%28r%29%5E3%29%2F2

==> 8 = r%5E3

==> +2%5E3+=+r%5E3

==> +2+=+r+


That is common ratio is 2.


Hope you found the explanation useful.

Regards.

Praseena.