SOLUTION: The sixth and 13th terms of a geometric progression are 5/2 and 320 respectively.Find the common ratio,the first term and the 10th term of this progression.

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Question 1186567: The sixth and 13th terms of a geometric progression are 5/2 and 320 respectively.Find the common ratio,the first term and the 10th term of this progression.
Answer by greenestamps(13195) About Me  (Show Source):
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6th term: ar%5E5=5%2F2

13th term: ar%5E12=320

The standard method for solving a problem like this, given two terms of a geometric sequence: Divide the second equation by the first

ar%5E12%2Far%5E5=320%2F%285%2F2%29
r%5E7=128
r=2

1st term: 6th term, divided by r^5
%285%2F2%29%2F%282%5E5%29=5%2F64

10th term: 13th term, divided by r^3
320%2F%282%5E3%29=40

ANSWERS:
1st term 5/64
10th term 40