How many three digit number which are divisible and multiply by 11
Answers
Answer:
Step-by-step explanation:Here is your answer !!
The first 3-digit number divisible by 11 is 110 .
The last 3-digit number divisible by 11 is 990 .
So , the A.P. series is 110 , 121 , .... 990 .
Common difference = 11 .
an = a1 + ( n - 1 ) d
=> 990 = 110 + ( n - 1 ) 11
=> 880 = ( n - 1 ) 11
=> 80 = ( n - 1 )
=> 81 = n .
So , number of 3 digit numbers divisible by 11 is 81 .
Now , the middlemost term is the 41th term .
So , a41 = a1 + ( n - 1 ) d [ where n = 41 ]
=> a41 = 110 + (41-1)*11
=> a41 = 110 + ( 11*40 )
=> a41 = 110 + 440
=> a41 = 550 .
So , the middlemost term of this A.P. series is 550
Answer:
Ast Three Digit Divisible By 11 = 990
First Three Digit Divisible By 11 = 110
Using Sum Of Ap
N/2(220+(N-1) 11) = N/2(110+990)
220+11n-11=1100
11n=880+11
N=81
Other Way Of Doing =
Subtracting (Three Digit + Two Digit Multiples) By Two Digit Multiples
Highest Three Digit Divisible By 11 = 990
= 11*90
Two Digit Highest = 99
=11*9
Therefore Three Digit Multiples Of 11 = 90-9 = 81