SOLUTION: find the first term in a geometric sequence which is such that the sum of the 1st and 3rd term is 50 and the sum of 2nd and 4th term is 150
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Question 931476: find the first term in a geometric sequence which is such that the sum of the 1st and 3rd term is 50 and the sum of 2nd and 4th term is 150 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! find the first term in a geometric sequence which is such that the sum of the 1st and 3rd term is 50 and the sum of 2nd and 4th term is 150
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1st + 3rd:: a + ar^2 = 50
2nd + 4th:: ar + ar^3 = 150
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Modify::
Multiply thru the 1st equation by "r" to get:
ar + ar^3 = 50r
ar + ar^3 = 150
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50r = 150
r = 3
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Solve for "a"::
a + ar^3 = 50
a(1+r^3) = 50
a(1+27) = 50
a(28) = 50
a = 25/14
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Ans: a = 25/14
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Cheers,
Stan H.
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