Question

What is the explicit formula for the following sequence 4,8,16,32,64?

Answer 1

In a geometric sequence, the ratio between two consecutive terms remains the same. In this case, this common ratio (r) is:

`r=(8)/(4)=(16)/(8)=(32)/(16)=(64)/(32)=2`

Therefore, the sequence is geometric.

Geometric sequence explicit formula

`a_n=a_1(r)^(n-1)`

where aₙ is the nth term, a₁ is the first term, and r is the common ratio.

In this case, the first term is a₁ = 4, and the common ratio is r = 2. Substituting these values into the formula, we get:

`a_n=4(2)^(n-1)`