Question

Find the sum of all multiple of 7 between 1 and 500

Answer 1

Answer:

VERIFIED ANSWER......

Step-by-step explanation:

The sum of all multiples of 7 between 0 and 500 is 17892

Step-by-step explanation:

To Find :The sum of all multiples of 7 between 0 and 500

Solution:

Multiples of 7 between 0 and 500 = 7,14,21,..........,497

This forms an AP

First term = a = 7

Common difference= 14-7 = 21-14 = 7

Formula of nth term = a_n=a+(n-1)dan=a+(n−1)d

So, 497=7+(n-1)7497=7+(n−1)7

497-7=(n-1)7497−7=(n−1)7

490=(n-1)7490=(n−1)7

70=(n-1)70=(n−1)

71=n71=n

Formula of first n terms = S_n=\frac{n}{2}(a+a_n)Sn=2n(a+an)

So,the sum of all multiples of 7 between 0 and 500=\frac{71}{2}(7+497)271(7+497)

                                                                                    =1789217892

Hence the sum of all multiples of 7 between 0 and 500 is 17892

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