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8th Term from Term Product (Posted on 2016-03-07) Difficulty: 3 of 5
The first three terms of sequence {C(n)} are 1440, 1716 and 1848. These are obtained by multiplying the corresponding terms of two arithmetic sequences:{A(n)} and {B(n)}.
Find the 8th term of {C(n)}

No Solution Yet Submitted by K Sengupta    
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Solution Solution | Comment 2 of 4 |
Define the terms of A(n) to be a + (n-1)*x for integer n, and similarly define the terms of B(n) to be b + (n-1)*y for integer n.  Then the terms of C(n) are ab + (n-1)*(ay+bx) + (n-1)^2*xy.

The first three terms of C(n) are given, so:
C(1) = ab = 1440
C(2) = ab + 1*(ay+bx) + 1*xy = 1716
C(3) = ab + 2*(ay+bx) + 4*xy = 1848

Treat this as a system of linear equations with variables ab, ay+bx, and xy.  Then solve to find:
ab = 1440
ay+bx = 348
xy = -72

Then C(8) = ab + 7*(ay+bx) + 49*xy = 1440 + 7*348 + 49*(-72) = 348.

  Posted by Brian Smith on 2016-03-07 12:33:12
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