Question

Hey dears !!!!


Q.1) How many two digit numbers are divisible by 4 ?



Q.2) How many three digit numbers are divisible by 4 ?


✡✡ Full explanation Answers needed ✡✡✡


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Answer 1

(1)

The first two digit number divisible by 4 = 12.

The last two digit number divisible by 4 = 96.

Let a be the first term and d be the common difference.

First term a = 12.

Last term an = 96

We know that an = a + (n - 1) * d

                        96 = 12 + (n - 1) * 4

                       84 =  4n - 4

                       88 = 4n

                       n = 22.


Therefore there are 22 two-digit numbers divisible by 4.



(2) 

The first 3-digit number divisible by 4 = 100

The last three digit number divisible by 4 = 996.

Let  a be the first term and d be the common difference.

First term a = 100

Common difference d = 4

Last term an = 996

We know that an = a + (n - 1) * d

                        996 = 100 + (n - 1) * 4

                        896 = 4n  - 4

                       900 = 4n

                       n = 900/4

                       n = 225.



Therefore there are 225 three digit numbers divisible by 4.


Hope this helps! 

Answer 2

hey dear




here is your answer



Solution


Explanation


2 digit numbers are between 10 to 99

first two digit number is divisible by 4 is 12



Last two digit number divisible by 4 is 96



sequence is 12 , 16 ,20 ......... 96


n is the number of term in the above Ap


a = 12

n = 96

d = 4


so

< n = a + ( n - 1 ) d >



Tn = 12 + ( n - 1 ) * 96


4 ( n -1 ) = 96 -12

4 ( n -1) = 84

n -1 = 84 /4

n - 1 = 21


so n = 21 +1

n = 22


hence your answer is 22



Next solution of question


The three digit natural number that are divisible by 4 are


100 , 104 , 108........... 996


it is an Ap where


a = t 1 = 100

d = 4


Let n take = 996


we know that for an ap


< n = a + (n - 1 ) * d >


996 = 100 + ( n - 1 ) *4



996 = 100 + 4n - 4



996 = 96 + 4n



996 -96 = 4n


900 = 4n



900 / 4 = n


so n = 225



hence your next answer is 225



hope it helps


thank you