Question

数列{an}满足an+1=an+n,且a1=1,则a5的值为?

an+1中 1为下脚标

Answer 1

a(n+1)=a(n)+n=a(n)+[n(n+1)-(n-1)n]/2,
a(n+1)-n(n+1)/2 = a(n) - (n-1)n/2 = ... = a(1) - 0 = 1,
a(n)= 1 + (n-1)n/2,
a(5)=1+4*5/2=11