Question

One of the following sequences is arithmetic and one is geometric. Identify which one is which, and write an explicit formula for each. Sequence #1: 4, 20, 100, 500. What is the explicit formula?

Answer 1

Answer: an = 4 × 5^(n - 1)

Step-by-step explanation:

The given sequence is a geometric sequence because consecutive terms differ by a common ratio. The

formula for determining the nth term of a geometric progression is expressed as

an = a1r^(n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a1 = 4

r = 20/4 = 100/20 = 5

Therefore, the explicit formula for the sequence is

an = 4 × 5^(n - 1)