general term of 2,7,14, 23 ..
回答 (3)
2011-11-12 2:23 am
✔ 最佳答案
T(1)=4-2T(2)=9-2
T(3)=16-2
T(4)=25-2
General Term T(x)=(x+1)^2 - 2
2011-11-12 3:59 am
a(n) - a(n - 1) = 5 + 2(n - 2)
a(n)
= 5 + 2(n - 2) + a(n - 1)
= 2 * 5 + 2[(n - 2) + (n - 3)] + a(n - 2)
= ...
= 5(n - 1) + 2[(n - 2) + (n - 3) ... + 1] + a(1)
= 5(n - 1) + (n - 1)(n - 2) + 2
= (n - 1)(n + 3) + 2
= n^2 + 2n - 1
a(n)
= 5 + 2(n - 2) + a(n - 1)
= 2 * 5 + 2[(n - 2) + (n - 3)] + a(n - 2)
= ...
= 5(n - 1) + 2[(n - 2) + (n - 3) ... + 1] + a(1)
= 5(n - 1) + (n - 1)(n - 2) + 2
= (n - 1)(n + 3) + 2
= n^2 + 2n - 1
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