Question

What is the sum of the multiples of 4 from 16 to 100?

Answer 1

Answer: Sum of the multiples of 4 from 16 to 100 is 1276.

Explanation:

Since we have given that

Multiples of 4 from 16 to 100:

`16,20,24,.....100`

First we find the number of terms (n):

Here a = first term = 16

d = common difference = 20-16=4

So, we know the formula for "nth term":

`a_n=a+(n-1)d\\\\100=16+(n-1)4\\\\100-16=(n-a)4\\\\(84)/(4)=n-1\\\\21=n-1\\\\n=21+1=22`

so, we need to calculate "Sum of 22 terms":

`S_(22)=(22)/(2)(2a+(n-1)d)\\\\S_(22)=11(2* 16+(22-1)4)\\\\s_(22)=11(32+21* 4)\\\\S_(22)=1276`

Hence, Sum of the multiples of 4 from 16 to 100 is 1276.

Answer 2

Correct answer is 1276.

This an arithmetic series.

`a_1=16,a_n=100,d=4,S_n=? \\ \\a_n=a_1+(n-1)d \\100=16+(n-1)4 \\4(n-1)=84 \\n-1=21 \\n=22 \\ \\S_n= ((a_1+a_n)n)/(2)= ((16+100)22)/(2)=116* 11=1276`