Answer:
The total number of two digit numbers that are divisible by 4 are 22.
Step-by-step explanation:
Step -1:
The two digit natural numbers starts from 10 and ends with 99.
Now, two digit numbers which are divisible by 4 are 12,16,20,…96.
Step -2:
Find number of terms of an Arithmetic Progression whose first term is 12 .
and common difference is 4.
Let a = 12 , d = 4
If the number of terms is n then an = 96
Now we know that, nth term of an A.P. is given by,
an = a+(n-1)d. --------(i)
where,
a= first term of A.P. , d= common difference, a
n =nth term of A.P.
Substituting values of a, d and an in equation (i) and we get,
96 = 12+(n−1) × 4
⇒ 96 − 12 = (n−1) × 4
⇒ 84 = 4n − 4
⇒ 84 +4 = 4n
⇒ 88 = 4n
⇒ n=22
Hence,
the total number of two digit numbers which are divisible by 4 is 22.
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Answers & Comments
The total number of two digit numbers that are divisible by 4 are 22.
Verified answer
Answer:
The total number of two digit numbers that are divisible by 4 are 22.
Step-by-step explanation:
Step -1:
The two digit natural numbers starts from 10 and ends with 99.
Now, two digit numbers which are divisible by 4 are 12,16,20,…96.
Step -2:
Find number of terms of an Arithmetic Progression whose first term is 12 .
and common difference is 4.
Let a = 12 , d = 4
If the number of terms is n then an = 96
Now we know that, nth term of an A.P. is given by,
an = a+(n-1)d. --------(i)
where,
a= first term of A.P. , d= common difference, a
n =nth term of A.P.
Substituting values of a, d and an in equation (i) and we get,
96 = 12+(n−1) × 4
⇒ 96 − 12 = (n−1) × 4
⇒ 84 = 4n − 4
⇒ 84 +4 = 4n
⇒ 88 = 4n
⇒ n=22
Hence,
the total number of two digit numbers which are divisible by 4 is 22.
Hope it help you . Please mark as brainlist.