SOLUTION: the sum of first two terms of a G P is x and the sum of last two terms is y. if there are nth terms in all find their common ratio

Question 1017337: the sum of first two terms of a G P is x and the sum of last two terms is y. if there are nth terms in all find their common ratio
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the nth term of a geometric sequence is defined
:
Xn = ar^(n-1) where a is the first term and r is the common ratio
:
we are given
X1 + X2 = x
a + ar = x
a = x / (r+1)
:
X(n-1) + Xn = y
ar^(n-2) + ar^(n-1) = y
:
now substitute for a
:
(x/(r+1))(r^(n-2) + (x/(r+1))(r^(n-1)) = y
:
xr^(n-2) + xr^(n-1) = y(r+1)
:
xr^(n-1)(r+1) = y(r+1)
:
xr^(n-1) = y
:
r^(n-1) = y / x
:
***********************
r = (y / x)^(1 / (n-1))
***********************

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