Question

What is the recursive formula of:
6,7,7.5,7.75,7.875,7.9375

Answer 1

Hello,


`a_(1)=6`

`a_(2)=7=a_(1)+1`

`a_(3)=7.5=a_(2)+ (1)/(2)=a_(1)+1+(1)/(2)=a_(1)+(((1)/(2))^3-1)/((1)/(2)-1)`


`a_(n)=a_(1)+(((1)/(2))^(n)-1)/((1)/(2)-1)=a_(1)+(2^n-1)/(2^(n-1))`