The weight of 5 members is measured in sequence and each time the average weight is increased by 1 kg. Find the difference between weight of first & last member

Answer

To find the difference between the weight of the first and the last member when the average weight of 5 members is increased by 1 kg each time, we can follow these steps:

### Step 1: Define the weights of the members
Let's denote the weight of the first member as \( x \). Since the average weight increases by 1 kg for each subsequent member, we can express the weights of the members as follows:
- Weight of 1st member = \( x \)
- Weight of 2nd member = \( x + 1 \)
- Weight of 3rd member = \( x + 2 \)
- Weight of 4th member = \( x + 3 \)
- Weight of 5th member = \( x + 4 \)

### Step 2: Calculate the average weight
The average weight of these 5 members can be calculated using the formula for average:
\[ \text{Average} = \frac{\text{Sum of weights}}{\text{Number of members}} \]
The sum of the weights is:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10 \]
Thus, the average weight is:
\[ \text{Average} = \frac{5x + 10}{5} = x + 2 \]

### Step 3: Analyze the increase in average weight
According to the problem, the average weight increases by 1 kg each time a new member's weight is measured. This means that the average weight of the last member (5th member) is:
\[ \text{New Average} = (x + 2) + 1 = x + 3 \]

### Step 4: Find the weight of the last member
The weight of the last member (5th member) is \( x + 4 \).

### Step 5: Calculate the difference between the first and last member's weight
Now, we need to find the difference between the weight of the first member and the last member:
\[ \text{Difference} = \text{Weight of 5th member} - \text{Weight of 1st member} = (x + 4) - x = 4 \]

### Conclusion
The difference between the weight of the first and last member is \( 4 \) kg.

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