Answer:
9, 18, 36, 72, 144.
Explanation:
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
In this case, the first term (a₁) is 9, and the common ratio (r) is 2.
The formula to find the nth term of a geometric sequence is given by:
aₙ = a₁ * r^(n-1)
Let's find the first five terms:
n = 1:
a₁ = 9 * 2^(1-1) = 9 * 2^0 = 9 * 1 = 9
n = 2:
a₂ = 9 * 2^(2-1) = 9 * 2 = 18
n = 3:
a₃ = 9 * 2^(3-1) = 9 * 4 = 36
n = 4:
a₄ = 9 * 2^(4-1) = 9 * 8 = 72
n = 5:
a₅ = 9 * 2^(5-1) = 9 * 16 = 144
So, the first five terms of the geometric sequence with a first term of 9 and a common ratio of 2 are: 9, 18, 36, 72, 144.