# Find the sum of a

Multiples of 7 lying between 500 and 900 are;

504, 511, 518…… 896

So,

Sum of all the multiples of 7 lying between 500 and 900 = 504 + 511 + 518…. + 896

d = 7

a = 504

a + (n – 1)d = 896

504 + (n – 1)7 = 896

504 + 7n – 7 = 896

7n = 896 + 7 – 504

7n = 399

n = 399/7 = 57

So,

Sum of 57 multiples = n/2[2a + (n – 1)d]

S57 = 57/2[2(504) + (57 – 1)(7)]

= 57/2 ×(1008 + 392)

= 57×700 = 39, 900

Hence,

Sum of all the multiples of 7 lying between 500 and 900 is 39,900.

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