How many three digit numbers are divisible by 11

Asked by admin @ 13/08/2021 in Math viewed by 303 People

How many three digit numbers are divisible by 11?Also find the middle term

Answered by admin @ 13/08/2021

Heya user ,
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 .

Hope it helps !!

How many three digit numbers are divisible by 11

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