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:

$r=\frac{8}{4}=\frac{16}{8}=\frac{32}{16}=\frac{64}{32}=2$

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:

$a_n=4(2)^{n-1}$