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: $7, 14, 21, \dots, (7 \times 350)$.
Sequence Properties:- 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.
Important Questions from Average (Notes)
- Average age of 20 students of a class is 10 years. Average age of these students together with their five teachers is 14. The age of Ramesh Sir, one of their five teachers, is exactly the same as the average age of all their five teachers. The sum of the ages (in years) of all the students and Ramesh Sir is
- The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?
- If the average of six consecutive even numbers is 13, then the average of the next three even numbers is:
एक परिवार में, पिता और माता की औसत आयु 35 वर्ष है । पिता, माता और उनके इकलौते बेटे की औसत आयु 27 वर्ष है । बेटे की उम्र _____________ है।
- 5 क्रमागत संख्याओं का औसत n है । यदि अगली दो संख्याएँ भी शामिल कर ली जाएँ, तो 7 संख्याओं का औसत
