Thread: Sequence

How would I find the third term in the recursively defined sequence: a[sub 1]=3, a[sub k+1]=a[sub k](a[sub k]-1).

Originally Posted by mike1

How would I find the third term in the recursively defined sequence: a[sub 1]=3, a[sub k+1]=a[sub k](a[sub k]-1).

let a[sub1] be a_1
let a[subk] be a_k
let a[sub k+1] be a_(k+1)

so the third term will have the formula:
a_3 = a_(2 + 1) = a_2 * (a_2 - 1) ..........but what is a_2? let's find out

a_2 = a_1 * (a_1 - 1) = 3*(3-1) = 3*2 = 6

=> a_3 = 6*(6 - 1) = 6*5 = 30