arithmetric?

2007-06-12 10:59 pm
Which of the following represents the sum of the first n terms of an arithmetic sequence with common difference 4?

answers:2(n^2)+n

回答 (1)

2007-06-12 11:35 pm
✔ 最佳答案
I think the question is MC question, better typing the choice.

First, find the n term.

T(n)=S(n)-S(n-1)
.....=2(n^2)+n -[2((n-1)^2)+(n-1)]
.....=2(n^2)+n-[2(n^2)-4n+2+n-1]
.....=2(n^2)+n-2(n^2)+3n-1
.....=4n-1

common difference=T(n)-T(n-1)
...........................=4n-1-[4(n-1)-1
...........................=4n-1-[4n-4-1]
...........................=4n-1-4n+5
...........................=4

Remark:
T(n) : n term
S(n): sum of the first terms


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