Question

6,10,16,24第n个数是多少

Answer 1

a1=6

a2=10=6+4=6+2×2

a3=16=10+6=10+2×3

a4=24=16+8=16+2×4

第n个数

an=a(n-1)+2n

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

=...

=a1+2n+2(n-1)+...+2×2

=4+2+2×2+2×3+...+2n

=4+2(1+2+3+...+n)

=4+n(n+1)

=n^2+n+4

an=n^2+n+4