Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 72, 18, 9 divided by 2, 9 divided by 8, ...

Answer 1

Missing number: Between 72 and 18, there should be 36. Therefore, the series should look like this:
72, 36, 18, 9, 9/2 9/8, ...

This is a geometric sequence in which;
a = 72
r = 1/2

Therefore, explicit formula is;
a(n) = a(1/2)^n

Since,
r lies between 1 and -1, the sequence converges at a/(1-r). That is,
=> a/(1-r) = 72/(1-1/2) = 72/(1/2) = 72*2 = 144