Finding a formula for a sequence

Jul 2008
212
2
Find a simple formula which defines the nth term of a sequences whose first few terms are the same as those given:

1, -4, 9, -16

I already know the answer is -(-1)^n * n^2

But how would I show working out?
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
\(\displaystyle 1, -4, 9, -16, \dots =1^2, -2^2, 3^2, -4^2, \dots =-(-1)^1\times 1^2, -(-1)^2\times 2^2, -(-1)^3\times \) \(\displaystyle 3^2, -(-1)^4\times 4^2, \dots \)
 
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