# What are the first three terms of a geometric sequence in which the first term is 4 and the common ratio is 5?

When the ratio between two consecutive terms is the same throughout the sequence that sequence is defined as a geometric sequence.

## Answer: 4, 20, 100 are the first three terms of a geometric sequence in which the first term is 4 and the common ratio is 5.

Let's find out the answer step by step.

**Explanation: **

Given:

first term (a) = 4

common ratio (r) = 5

The formula for the n^{th} term for a geometric sequence is given as,

a_{n} = a.r^{n-1}

where,

first term=(a)

common ratio=(r)

Now, put the values in geometric sequence formula,

a_{1} = 4.5^{1-1 }= 4.1 = 4

a_{2} = 4.5^{2-1} = 4.5 = 20

a_{3} = 4.5^{3-1} = 4.25 = 100

Therefore, the first three terms are 4, 20, 100