If the mean of `7` consecutive multiples of `3` is `18`, find the `4`th and `5`th numbers.

Options

A. `25,26`
B. `18,21`
C. `11,12`
D. `28,29`

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the problem
We need to find the 4th and 5th numbers of 7 consecutive multiples of 3, given that their mean is 18.

### Step 2: Define the consecutive multiples of 3
Let the first multiple of 3 be represented as \(3x\). Therefore, the 7 consecutive multiples of 3 can be expressed as:
- 1st number: \(3x\)
- 2nd number: \(3x + 3\)
- 3rd number: \(3x + 6\)
- 4th number: \(3x + 9\)
- 5th number: \(3x + 12\)
- 6th number: \(3x + 15\)
- 7th number: \(3x + 18\)

### Step 3: Calculate the mean
The mean of these numbers is given by the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
Here, the mean is given as 18 and the number of observations is 7.

### Step 4: Set up the equation for the mean
The sum of the 7 numbers is:
\[ 3x + (3x + 3) + (3x + 6) + (3x + 9) + (3x + 12) + (3x + 15) + (3x + 18) \]
This simplifies to:
\[ 21x + (3 + 6 + 9 + 12 + 15 + 18) = 21x + 63 \]
Thus, we can set up the equation:
\[ \frac{21x + 63}{7} = 18 \]

### Step 5: Solve for \(x\)
Multiplying both sides by 7 gives:
\[ 21x + 63 = 126 \]
Now, subtract 63 from both sides:
\[ 21x = 126 - 63 \]
\[ 21x = 63 \]
Now, divide by 21:
\[ x = \frac{63}{21} = 3 \]

### Step 6: Find the 4th and 5th numbers
Now that we have \(x = 3\), we can find the 4th and 5th numbers:
- 4th number: \(3x + 9 = 3(3) + 9 = 9 + 9 = 18\)
- 5th number: \(3x + 12 = 3(3) + 12 = 9 + 12 = 21\)

### Final Answer
The 4th number is **18** and the 5th number is **21**.

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