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


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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

	$f i r s t t h r e e d i g i t n u m b e r d i v i s b l e b y 7 i s = 105$ $s e c o n d i s = (105 + 7 = 112)$ $. . .$ $. . .$ $l a s t t h r e e d i g i t n u m b e r d i v i b l e b y 7 = 994$ $s o S = 105 + 112 + . . . + 994$ $i n A . p s e r i e s a = 105 d = 7$ $a + (n - 1) 7 = 994$ $105 + (n - 1) 7 = 994$ $n - 1 = \frac{994 - 105}{7} = \frac{889}{7} = 127$ $n = 128$ $S = \frac{n}{2} [2 a + (n - 1) d]$ $= \frac{128}{2} [a + a + (n - 1) d]$ $= \frac{128}{2} [105 + 994] = 70336$
	Answered by mr W last updated on 29/Mar/19

	$A . P . :$ $105, 112, 119, . . ., 994$ $n = \frac{994 - 105}{7} + 1 = 128$ $Σ = \frac{(105 + 994) \times 128}{2} = 70336$
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