# Math

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1) If the sum of the first n terms of a series is Sn where Sn=2n²-n,
(a)prove that the series is an AP, stating the first term and the common difference;
(b)find the sum of the terms from the 3rd to the 12th inclusive

2) In an AP the 6th term is half the 4th term and the 3rd term is 15.
(a)Find the first term and the common difference;
(b)How many terms are needed to give a sum that is less than 65?

• Math -

Isn't t(n) = S(n) - S(n-1)

(e.g. the sixth term is sum of 6 terms minus the sum of 5 terms)

so t(n) = 2n^2-n - (2(n-1)^2 - (n-1))
= 4n - 3

so from that you can now find any of the terms
notice t(1) = a = 1
d = 4
2) "the 6th term is half the 4th term"
----> a+5d = 1/2(a+3d)

"the 3rd term is 15" -----> a+2d = 15

solve these two equations.

• LA PRINCE HIGH SCHOOL -

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