SOLUTION: The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the pro

Algebra ->  Sequences-and-series -> SOLUTION: The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the pro      Log On


   

Question 1005464: The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the progression.
Answer by stanbon(75887) About Me  (Show Source):
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The sum of the 6th and 8th terms of an A.P is 142 . If the fourth term is 49 , (a) find the first term . (b) the common difference . (c) the sum of the first seven terms of the progression.
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6th term:: a(1)+5d
8th term:: a(1)+7d
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Equation:
sum = 142
2*a(1) + 12d = 142
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a(1) + 6d = 71
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4th term:: a(1) + 3d = 49
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Equations:
a(1) + 6d = 71
a(1) + 3d = 49
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Subtract and solve for "d"::
3d = 22
d = 22/3
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Solve for a(1)::
a(1) + 3d = 49
a(1) + 22 = 49
a(1) = 27
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Sum the 1st 7 terms:
S(7) = (7/2)(a(1)+a(7)]
S(7) = (7/2)(27+71)
S(7) = (7/2)(98)
S(7) = 7*49 = 343
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Cheers,
Stan H.