Question

What is the explicit formula for this geometric sequence?

f 1 2 3 4 5 6
f(n) 1 2 4 8 16 32

Answer 1

So the values we have are:

n : 1 2 3 4 5 6

and

f(n) : 1 2 4 8 16 32

Thus, the explicit formula for this geometric sequence is :

f(n) = $2^{n-1}$

Thus, on substituting the values of n provided to us:

When n = 1, f(1) = $2^{1-1} = 2^0 = 1$

When n = 2, f(2) = $2^{2-1} = 2^1 = 2$

When n = 3, f(3) = $2^{3-1} = 2^2 = 4$

and so on...