Question

求等差数列1,2,4,7,11,16.的通式?

Answer 1

1+1=2,2+2=4,4+3=7.

a1=1,a2=a1+1,a3=a2+2.

an=a(n-1)+(n-1)

=a(n-2)+(n-2)+(n-1)

=a(n-3)+(n-3)+(n-2)+(n-1)

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=a1+1+2+3+...+(n-1)

=1+n(n-1)/2