SOLUTION: The sum of the first 7 terms of an A.P is 28 and the sum of the first 15 terms is 90. Find the sum of the n term

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Question 856229: The sum of the first 7 terms of an A.P is 28 and the sum of the first 15 terms is 90. Find the sum of the n term
Answer by richwmiller(17219) About Me  (Show Source):
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S = ½(a + an)n
S = ½(2a + (n-1)d)n
an = a + (n - 1)d
S = ½(2a + (n-1)d)n
28= ½(2a + 6d)7
90 = 1/2(2a+ 14d)15
28=(a + 3d)7,
90 = (a+ 7d)15
a = 5/2, d = 1/2
S = ½(5/2 + An)n
or
S = ½(2*5/2 + 1/2(n-1))n
S = 1/4 n(n+9)