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Write the first five terms of the geometric sequence whose first term is 9, and whose common ratio is 2.

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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.

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