# Given the sequence a_0=1,a_1=2, a_(k+1)=a_k+(a_(k-1))/(1+a_(k-1)^2), k > 1 for what value of k occours 52 < a_k < 65 ?

Oct 12, 2017

I used column A for my value of k. I entered 0 in cell A1 and I entered =A1+1 in cell A2; this will give me a column of integers incremented by 1 as I copy and block paste the column.

I used column B for my value of ${a}_{k}$. I entered 1 in cell B1, 2 in cell B2, and =B2+B1/(1+B1^2) in cell B3; this will give me the recursive calculation as I copy and block paste the column.

The first value of k where $52 < {a}_{k} < 65$ is:

$k = 1350 , {a}_{k} = 52.01277$

The last value of k where $52 < {a}_{k} < 65$ is:

$k = 2109 , {a}_{k} = 64.98885$