SOLUTION: the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms is 3 find the terms of gp

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Question 773910: the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms is 3 find the terms of gp
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Q:
the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms is 3 find the terms of gp
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A:
Let x = first term
and r = common ratio
Therefore, rx = second term
r%5E2x = third term
r%5E3x = fourth term
x+%2B+rx+%2B+r%5E2x+%2B+r%5E3x = 7.5
x%281+%2B+r%29+%2B+r%5E2x%281+%2B+r%29 = 7.5
%281+%2B+r%29%28x+%2B+r%5E2x%29 = 7.5
x%281+%2B+r%29%281+%2B+r%5E2%29 = 7.5
The sum of the middle two terms is
rx+%2B+r%5E2x = 3 ---> rx(1 + r) = 3 ---> x = 3%2Fr%281%2Br%29
%283%2Fr%281%2Br%29%29%281+%2B+r%29%281+%2B+r%5E2%29 = 7.5
%283%2Fr%28cross%281%2Br%29%29%29%28cross%281+%2B+r%29%29%281+%2B+r%5E2%29 = 7.5
1+%2B+r%5E2 = 7.5%28r%2F3%29
r%5E2+-+2.5r+%2B+1+=+0
2r%5E2+-+5r+%2B+2+=+0
(2r - 1)(r - 1) = 0
r = 1%2F2 or r = 1, disregard r = 1
If r = 1/2, then x = 3%2F%281%2F2%29%281%2B%281%2F2%29%29 = 4
The first term is 4, to get the next term, multiply by the common ratio 1/2.
The first 4 terms are highlight%284%29, highlight%282%29, highlight%281%29, and highlight%281%2F2%29.