What are the first three terms of a geometric sequence with a first term of 4 and a common ratio of 5?

A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

In this case:

• First term (a): 4
• Common ratio (r): 5

To find the first three terms of the geometric sequence, we can use the formula for the nth term of a geometric sequence, which is given by:

a_n = a * r^(n-1)

Using this formula, we can find the first three terms:

1. First term (n = 1):
• a₁ = 4 * 5^(1-1) = 4 * 5⁰ = 4 * 1 = 4
2. Second term (n = 2):
• a₂ = 4 * 5^(2-1) = 4 * 5¹ = 4 * 5 = 20
3. Third term (n = 3):
• a₃ = 4 * 5^(3-1) = 4 * 5² = 4 * 25 = 100

Therefore, the first three terms of the geometric sequence are:

4, 20, and 100.