SOLUTION: Find sum of 9 terms in a
arithmetic sequence is 207 sum of first 20 terms
is 900 . Find fifth and twenty fifth term Find
the sum of 100 terms
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arithmetic sequence is 207 sum of first 20 terms
is 900 . Find fifth and twenty fifth term Find
the sum of 100 terms
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Question 1042037: Find sum of 9 terms in a
arithmetic sequence is 207 sum of first 20 terms
is 900 . Find fifth and twenty fifth term Find
the sum of 100 terms Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! If the sum of 9 terms in an arithmetic sequence is 207 and the sum of first 20 terms is 900 ,
Find fifth and twenty-fifth term
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S(9) = (a(1)+(a(1)+8d)*(9/2) = 207
S(20) = (a(1)+(a(1)+19d)*(20/2) = 900
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2(a(1)) + 8d = (2/9)207 = 2*23 = 46
2(a(1)) + 19d = 90
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Subtract and solve for "d"::
11d = 44
d = 4
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Then, solve for a(1)::
2*a(1) + 8d = 46
2*a(1) + 32 = 46
a(1) = 7
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Ans: a(5) = 7 + 4d = 7 + 16 = 23
a(25) = 7 + 24d = 7 + 96 = 103
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Find the sum of 100 terms.
s(100) = (7 + a(100))*(50)
a(100) = 7 + 99*4 = 403
S(100) = 410*50 = 20500
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Cheers,
Stan H.
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