Average of Multiples of 7 Calculation

The question requires finding the average value of the first 350 positive multiples of 7.

The sequence formed by the first 350 positive multiples of 7 is an arithmetic progression: $7, 14, 21, \dots, (7 \times 350)$.

• First Term ($a$): The first multiple is $7 \times 1 = 7$.
• Number of Terms ($n$): There are $350$ multiples.
• Last Term ($l$): The last multiple is $7 \times 350 = 2450$.

Arithmetic Progression Average Formula

For an arithmetic progression, the average (mean) value is calculated by adding the first and last terms and dividing by 2.

The formula is:

Average = $\frac{\text{First Term} + \text{Last Term}}{2}$ = $\frac{a + l}{2}$

Substitute the identified values into the formula:

Average = $\frac{7 + 2450}{2}$

Perform the calculation:

Average = $\frac{2457}{2} = 1228.5$

The average value of the first 350 positive multiples of 7 is 1228.5.