Question

Find the number of all three digit natural numbers which are divisible by 9.

Answer 1

100 is the answer

Here's the explanation:he lowest number greater than a hundred and divisible by 9 is 108... the largest number divisible by 9 and less than a thousand is 999... 

we use this formula... 

T = A + (n-1)*d 

T is the nth term in an arithmetic sequence 
A is the first term in an arithmetic sequence 
n is the number of terms 
d is the common difference 

you are asking for "the number of 3 digit numbers divisible by 9" or numbers that are greater than 100 but less than 1000 that are divisible by 9 

so... 

we are looking for the number of terms given 

first term(A) = 108 
last term(T) = 999 
common difference(d) = 9 

we subtitute the given values 
999 = 108 + ( n - 1 ) * 9 

we then solve... 
999 = 108 + ( n - 1 ) * 9 
999 - 108 = ( n - 1 ) * 9 
891 = ( n - 1 ) * 9 
( 891 ) / 9 = [ ( n - 1 ) * 9 ] / 9 
99 = n - 1 
99 + 1 = n 
100 = n 

therefore... 
there are 100 3-digit numbers divisible by 9 

hope this helps!!!Source(s):My brain!!! 
I really have nothing to do...

Answer 2

$\: \red {\boxed { \huge \frak{ \star \: Hola! \: Mate \: \star}}} \\ \\ \: \: \: \: \: \: \orange{ \underline{ \mathbb{✓ \: Here \: Is \: Your \: Answer \: ✓ }}} \: \\ \\ \tiny \frak{the \: ap's \: are : 108,117,126,.......999} \\ \\ \underline{\bf{GIVEN}} : \\ \\ \tiny \bf{a =108,d = a2 - a1 = 117 - 108 = 9 \:and \: last \: term \: = 999} \\ \\ \underline{ \bf{we \: know \: the \: formula \: as \: followed }} \\ \\ \rightarrow \: \bf{ a \tiny{n} = a + (n - 1) \times d} \\ \\ \rightarrow \frak{ 999 =108 + (n - 1) \times 9} \\ \\ \rightarrow \frak{999 = 108 + 9n - 9} \\ \\ \rightarrow \frak{999 = 99 + 9n} \\ \\ \rightarrow \frak{999 - 99 = 9n} \\ \\ \rightarrow \frak{ 900 = 9n} \\ \\ \frak{9n = 900} \\ \\ \frak{n = \frac{ \cancel{900}}{ \cancel{9 \: \: }} } = 100 \\ \\ \rightarrow \frak{n = 100} \\ \\ \pink {\underline{\tiny\mathcal{THERE \: ARE \: 100 \: OF \:three\:digits\: NUMBERS \: WHICH \: ARE \: DIVISIBLE \: OF \: 9.}}}$