The mean of 5 consecutive multiples of 7 is 28. Find the sum of 2nd and 3rd numbers.

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and break it down clearly:

### Step 1: Understand the Problem
We need to find the sum of the 2nd and 3rd consecutive multiples of 7, given that the mean of 5 consecutive multiples of 7 is 28.

### Step 2: Define the Consecutive Multiples
Let the first multiple of 7 be represented as \(7x\). The next four consecutive multiples can be expressed as:
- 1st number: \(7x\)
- 2nd number: \(7x + 7\)
- 3rd number: \(7x + 14\)
- 4th number: \(7x + 21\)
- 5th number: \(7x + 28\)

### Step 3: Calculate the Mean
The mean of these five numbers is given by the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
We know the mean is 28, and the number of observations is 5.

### Step 4: Set Up the Equation
The sum of the five numbers is:
\[ 7x + (7x + 7) + (7x + 14) + (7x + 21) + (7x + 28) \]
This simplifies to:
\[ 7x + 7x + 7 + 7x + 14 + 7x + 21 + 7x + 28 = 35x + 70 \]
Now, we can set up the equation for the mean:
\[ \frac{35x + 70}{5} = 28 \]

### Step 5: Solve for \(x\)
Multiply both sides by 5:
\[ 35x + 70 = 140 \]
Now, subtract 70 from both sides:
\[ 35x = 70 \]
Divide by 35:
\[ x = 2 \]

### Step 6: Find the 2nd and 3rd Numbers
Now that we have \(x = 2\), we can find the 2nd and 3rd numbers:
- 2nd number:
\[ 7x + 7 = 7(2) + 7 = 14 + 7 = 21 \]
- 3rd number:
\[ 7x + 14 = 7(2) + 14 = 14 + 14 = 28 \]

### Step 7: Calculate the Sum of the 2nd and 3rd Numbers
Now, we find the sum of the 2nd and 3rd numbers:
\[ 21 + 28 = 49 \]

### Final Answer
The sum of the 2nd and 3rd numbers is **49**.

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