Question

How many multiples of $6$ are between $100$ and $500$?

Answer 1

ANSWER

65

EXPLANATION

This will form a sequence with first term:

$a_{1} = 102$

with constant difference d=6 and last term

$l = 486$

The last term is a term in the sequence, therefore;

$l=a_1+d(n-1)$

$486=102+6(n-1)$

$486 - 102 = 6(n-1)$

Simplify the LHS

$384= 6(n-1)$

Divide both sides by 6.

$64=n-1$

$64 + 1 = n$

Therefore

$n = 65$

Hence there are 65 multiples of 6.

Answer 2

Answer:

67

Step-by-step explanation:

First number between 100 to 500 which is divisible by 6 is 102

Multiples of 6 between 100 to 500 :

102,102+6,102+6+6,....

This Forms an AP

a= first term = 102

d = common difference = 6

Last number between 100 to 500 which is divisible by 6 is 498

So, $a_n=498$

Formula of nth term = $a_n=a+(n-1)d$

$498=102+(n-1)6$

$498-102=(n-1)6$

$396=(n-1)6$

$\frac{396}{6}=n-1$

$66=n-1$

$66+1=n$

$67=n$

Hence there are 67 multiples of 6 between 100 to 500.