Question

What is the average of all the multiplies of 5 from 102 to 298 ?
A) 150
B) 200
C) 250
D) 100​

Answer 1

C) 250

hope this helps you

Answer 2

Given:

Multiples of 5 from 102 to 298

To find:

The average of all such multiples

Solution:

The average of all the multiplies of 5 from 102 to 298 is 200. (Option B)

We can find the average by following the given steps-

We know that the multiples of 5 form an arithmetic progression with the common difference of 5.

The lowest multiple of 5 between 102 and 298 is 105.

Similarly, the highest multiple of 5 between 102 and 298 is 295.

So, the A.P. becomes 105, 110, 115, and so on till 295.

So, the first term of the A.P., a=105

The last term of the A.P., l=295

The common difference, d=5

We will find the number of terms of the A.P. as follows-

The number of terms of the A.P., n=((Last term-First term)/ common difference)+1

=(295-105)/5+1

=390/5+1

=78+1

=79

Now, the sum of the terms in A.P.=n/2(a+l)

On putting the values,

Sum=79/2(105+295)

=79/2(400)

=79×200

Now, the average of all the multiples of 5 between 102 and 298=Sum of all the multiples/Number of multiples

=Sum/n

=79×200/79

=200

Therefore, the average of all the multiplies of 5 from 102 to 298 is 200.