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Find the sum of all natural numbers less than 500 that are devisible by 7

Find the sum of all natural numbers less than 500 that are devisible by 7

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
If we divide 500 by 7, we get 3 as remainder.
That means if we subtract 3 from 500, the number formed
will be divisible by 7.
Hence if we make a series of numbers divisible by 7,
7,14,21,28,.........497
We have to calculate the sum of this series.
This is an A.P.
In which a= 7, d =7
So
Tn = a+ (n-1)*d 
497 = 7 + (n-1)*7
490/7 = (n-1)
n = 71
Hence this A.P. contains 71 terms.
Now S71 = (71/2)[7+ 497]
 = 71*504/2
 = 17892
 

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