How many multiples of 4 lie between 10 and 25 | vedclass

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(D) The first multiple of $4$ greater than $10$ is $12$. The next multiples are $16, 20, 24, \ldots$These terms form an Arithmetic Progression $(A.P.)

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(D) The first multiple of $4$ greater than $10$ is $12$. The next multiples are $16, 20, 24, \ldots$These terms form an Arithmetic Progression $(A.P.)$ where the first term $a = 12$ and the common difference $d = 4$.To find the last term,we divide $250$ by $4$. Since $250 = 4 	imes 62 + 2$,the remainder is $2$. Therefore,the largest multiple of $4$ less than or equal to $250$ is $250 - 2 = 248$.We have the $A.P.$ series: $12, 16, 20, 24, \ldots, 248$.Using the formula for the $n^{	ext{th}}$ term of an $A.P.$: $a_n = a + (n - 1)d$Substituting the values: $248 = 12 + (n - 1)4$$248 - 12 = (n - 1)4$$236 = (n - 1)4$$n - 1 = \frac{236}{4}$$n - 1 = 59$$n = 60$Thus,there are $60$ multiples of $4$ between $10$ and $250$.

How many multiples of $4$ lie between $10$ and $250$?

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