The average of the first 20 multiples of 7 is {fill_ number}.

Question

The average of the first 20 multiples of 7 is {fill_ number}.

Accepted Answer

Concept- The average is 73.5. A number that is entirely divisible by the original number is referred to as a multiple of that number. Therefore, we must first identify the first twenty multiples of 7, after which we must attempt to create series utilizing these multiples. Once a clear series has been established, we can use some helpful formulas to get the average of the first 20 multiples of 7.
If two numbers, a and b, are multiplied in elementary mathematics, then b is the multiple of a. Therefore, the definition of multiple is the product obtained from multiplying two numbers.
For instance, the sum of 3 and 4 is equal to 12, hence 12 is a multiple of both 3 and 4.
The number 7 is offered to us in our dilemma. The average of the first 20 multiples of 7 must be determined.
Multiples of 7 are therefore:

71, 72, 73, 74 . . . . . . . . . . . . . . . . . . . 720 .

We attempt to construct a series by paying particular attention to the variables that are multiples of 7.
Now, by selecting 7 common from the multiples, a recurrent pattern might be created.
Seven frequent multiples yield the following:

7 (1 + 2 + 3 + 4 . . . . . . . . . . . . . . . . . . . + 19 + 20)

The series formula yields

Sn = \frac{n (n + 1)}{2}

Therefore, there are 20 terms in our example for the first 20 multiples.
So, the total would be: 7⋅

\frac{20 (20 + 1)}{2}

=1470

A = \frac{1470}{20} = 73.5

We now divide the sum by the total number of terms, or 20, to determine the average.
Therefore, 73.5 is the average of the first 20 multiples of 7.
Hence, the correct option is

73.5

.
ExamType: CBSE

The average of the first $20 multiples of 7$ is {fill_ number}.

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