Question 1176312: In a geometric progression the 5th term is 9 times the 3rd term and the sum of the 6th and 7th terms is 1944. Determine (a) the common ratio,(b) the 1st term
and (c) the sum of the 4th to 10th terms inclusive.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The nth term of a G.P. is a_n = a*r^(n-1), where a is the 1st term and r is the
common ratio.
Since a_5 = 9*a_3, we have ar^4 = 9ar^2 -> r^2 = 9
There are two possibilities: r = 3, or r = -3
If r = 3, a_6 + a_7 = 1944 = a(3)^5 + a(3)^6 -> a = 1944/((3)^5 + (3)^6)) = 2
If r = -3, a = 1944/((-3)^5 + (-3)^6) = 4
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