The average of five consecutive numbers is a. If the next two numbers are also included, how will the average vary? Option 1: It shall increase by 1 Option 2: It shall increase by 1 * 4 Option 3: It shall remain the same Option 4: It shall increase by 2

Answer: It shall increase by 1. Solution: 1) Let's say first number is n. Then: - First 5 numbers: n, n+1, n+2, n+3, n+4 - Next 2 numbers: n+5, n+6 2) First 5 numbers average = a = (n + (n+1) + (n+2) + (n+3) + (n+4))/5 = a = (5n + 10)/5 = a = n + 2 = a 3) All 7 numbers average: = (n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) + (n+6))/7 = (7n + 21)/7 = n + 3 4) Difference between averages: = New average - Original average = (n + 3) - (n + 2) = 1 Therefore, the average will increase by 1.

Arithmetic

Averages

Easy

The average of five consecutive numbers is a. If the next two numbers are also included, how will the average vary?

It shall increase by 1

It shall increase by $1 \cdot 4$

It shall remain the same

It shall increase by 2

✅ Correct Option: 1

Let's say first number is n. Then:

First 5 numbers: n, n+1, n+2, n+3, n+4
- Next 2 numbers: n+5, n+6

First 5 numbers average = a

= $\frac{n + (n+1) + (n+2) + (n+3) + (n+4)}{5} = a$

= $\frac{5n + 10}{5} = a$

= $n + 2 = a$

All 7 numbers average:

= $\frac{n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) + (n+6)}{7}$

= $\frac{7n + 21}{7}$

= $n + 3$

Difference between averages:

= New average - Original average

= $(n + 3) - (n + 2)$

= $1$

Therefore, the average will increase by 1.

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The average of five consecutive numbers is a. If the next two numbers are also included, how will the average vary?

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