The sum of the 2nd and 5th terms of a geometric sequence is 3.5. The sum of the 3rd and 6th is -7. Determine the ratio r of the sequence and the first term a.

3 answers

ar + ar^4 = 7/2
ar^2 + ar^5 = -7

divide and you have

r(1+r^3) / r^2(1+r^3) = -1/2
1/r = -1/2
r = -2
So, a = 1/4

Check. The sequence is

1/4 -1/2 1 -2 4 -8
-1/2 + 4 = 7/2
1 + (-8) = -7

what are you dividing??

5th term and 6th term

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