Question

Write the explicit formula for the geometric sequence.

Answer 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 4 gives the next term. In other words:

 an = a1 * r ^ (n-1)

Now, knowing that a1 = 2, and r = 4

We check

a2 = 2 * 4 ^ (2-1) = 2 * (4 ^ 1) = 8

a3 = 2 * 4 ^ (3-1) = 2 * (4 ^ 2) = 32

a4 = 2 * 4 ^ (4-1) = 2 * (4 ^ 3) = 128

Therefore, this is the geometric function that this sequence fulfills.