find-the-sum-of-all-three-digital-natural-numbers-that-are-divisible-by-7-

Question Number 57062 by olalekan2 last updated on 29/Mar/19

f i n d t h e s u m o f a l l

t h r e e d i g i t a l n a t u r a l

n u m b e r s t h a t a r e

d i v i s i b l e b y 7

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Mar/19

Answered by tanmay.chaudhury50@gmail.com last updated on 29/Mar/19

f i r s t t h r e e d i g i t n u m b e r d i v i s b l e b y 7 i s = 105

s e c o n d i s = (105 + 7 = 112)

\dots

\dots

l a s t t h r e e d i g i t n u m b e r d i v i b l e b y 7 = 994

s o S = 105 + 112 + \dots + 994

i n A . p s e r i e s a = 105 d = 7

a + (n - 1) 7 = 994

105 + (n - 1) 7 = 994

n - 1 = \frac{994 - 105}{7} = \frac{889}{7} = 127

n = 128

S = \frac{n}{2} [2 a + (n - 1) d]

= \frac{128}{2} [a + a + (n - 1) d]

= \frac{128}{2} [105 + 994] = 70336

Answered by mr W last updated on 29/Mar/19

A . P . :

105, 112, 119, \dots, 994

n = \frac{994 - 105}{7} + 1 = 128

Σ = \frac{(105 + 994) \times 128}{2} = 70336

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