Q38 of 84 Page 5

Find the sum of all multiples of 7 lying between 500 and 900. ? (CBSE 2012)

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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