Question

How many numbers up to 500 are divisible by 23?

Answer 1

$23 , 46, \: 69 \: \cdot \cdot \cdot , 483 \: are \\divisible \: by \: 23 \: upto \: 500$

$It \: is \: an \: A.p$

$First \:term (a) = 23$

$Common \: Difference \:(d)\\ = a_{2} - a_{1} \\= 46 - 23 \\= 23$

$\boxed {\pink { n^{th} \:term (a_{n}) = a+(n-1)d }}$

$\implies a_{n} = 483$

$\implies 23 + (n-1)23 = 483$

/* Dividing each term by 23 , we get */

$\implies 1 + n - 1 = 21$

$\implies n = 21$

Therefore.,

$\red { Numbers \: up\: to \:500 \: are}\\\red{ divisible \:by\: 23} \green {= 21 }$

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