Question

What is the recursive formula for this sequence: 100,160, 226, 298.6,.. ?

Answer 1

It is explained below

Explanation:

Letting `a_1=100; a_2=160`, the recursive formula works out as follows:

`a_3 = a_2 + (a_2-a_1)+ (a_2-a_1)/10 = 21/10 a_2 -11/10 a_1`

`a_4= a_3 + (a_3-a_2)+ (a_3-a_2)/10 = 21/10 a_3 - 11/10 a_2`

and in general
`a_(n+1) = 21/10 a_n -11/10 a_(n-1)` for n>=2