Third Proportional Calculation for 9, 7, ?, 14

This problem asks us to find a missing number in a sequence where the numbers are related proportionally. The sequence given is 9, 7, ?, 14.

Proportion Basics Explained

A proportion is a statement that indicates that two ratios (or fractions) are equal. The standard form is a : b = c : d, which can also be written as ∕$a$ / ∕$b$ = ∕$c$ / ∕$d$.

Although the question uses the term "third proportional," the structure of the given numbers (9, 7, ?, 14) suggests we need to find the missing term (let's call it x) that maintains the proportion between the first two numbers and the last two numbers.

Setting Up the Proportion Equation

We assume the sequence follows the proportion a : b = c : d. In this case:

• a = 9
• b = 7
• c = x (the missing term)
• d = 14

So, the proportion can be written as:

9 : 7 = x : 14

Or in fractional form:

$$ \frac{9}{7} = \frac{x}{14} $$

Calculating the Missing Term

To find the value of x, we can solve the equation:

$$ \frac{9}{7} = \frac{x}{14} $$

To isolate x, we multiply both sides of the equation by 14:

$$ x = \frac{9}{7} \times 14 $$

Now, we can simplify the calculation:

$$ x = 9 \times \frac{14}{7} $$

$$ x = 9 \times 2 $$

$$ x = 18 $$

Therefore, the missing term in the proportion is 18.