find the missing spaces if this sequence is geometric: 3___6___12___24

To determine if the sequence \( 3, \_\_, 6, \_\_, 12, \_\_, 24 \) is geometric, we need to check if there's a constant ratio between consecutive terms. Let's denote the missing terms as \( x_1, x_2, x_3 \).

### Step-by-step approach:

A geometric sequence has the property that the ratio between consecutive terms is constant, i.e.,
\[
r = \frac{a_{n+1}}{a_n}
\]
where \( r \) is the common ratio.

1. The ratio between the first and third term is:
   \[
   r^2 = \frac{6}{3} = 2 \quad \Rightarrow \quad r = \sqrt{2} = 1.414
   \]

2. The ratio between the third and fifth term:
   \[
   r^2 = \frac{12}{6} = 2 \quad \Rightarrow \quad r = \sqrt{2} = 1.414
   \]

 steps adjusting steps,? result interval.

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Find the missing spaces if this sequence is geometric: 3___6___12___24

Solve for the missing terms in the geometric sequence 3, ___, 6, ___, 12, ___, 24 using the common ratio property. This step-by-step solution explains how to find the constant ratio and fill in the missing values. Suitable for students in Grades 8-10.

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