Question

1,7,17,31,49...则第n个数是多少?

Answer 1

1,7,17,31,49... 通项为an

差为:6,10,14,18. bn

差为:4,4,4,.

bn=4n+2

an-a(n-1)=4(n-1)+2=4n-2

a(n-1)-a(n-2)=4n-6

.

a3-a2=10

a2-a1=6

相加得

an-a1=6+10+...+(4n-6)+(4n-2)

=(6+4n-2)*(n-1)/2

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

an=2n^2-1.