how many numbers between 400 to 700 are divisible by 9 or 11 (exclusively)
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Answered by
8
Hi ,
i ) 405 ,414 , ...., 693 are numbers between
400 to 700 divisible by 9
This is clearly in A.P.
first term ( a ) = 405
common difference ( d ) = a2 - a1
d = 414 - 405 = 9
let number of terms = n
an = 693
a + ( n - 1 )d = 693
405 + ( n - 1 )9 = 693
divide each term with 9 , we get
45 + n - 1 = 77
n = 77 - 44
n = 33
ii ) 407 ,418 ,.... , 693 are numbers
between 400 to 700 divisible by 11.
It is clearly in A.P.
first term ( a ) = 407
common difference ( d ) = 11
an = 693
a + ( n - 1 )d = 693
407 + ( n - 1 ) 11 = 693
divide each term with 11 , we get
37 + n - 1 = 63
n = 63 - 36
n = 27
I hope this helps you.
: )
i ) 405 ,414 , ...., 693 are numbers between
400 to 700 divisible by 9
This is clearly in A.P.
first term ( a ) = 405
common difference ( d ) = a2 - a1
d = 414 - 405 = 9
let number of terms = n
an = 693
a + ( n - 1 )d = 693
405 + ( n - 1 )9 = 693
divide each term with 9 , we get
45 + n - 1 = 77
n = 77 - 44
n = 33
ii ) 407 ,418 ,.... , 693 are numbers
between 400 to 700 divisible by 11.
It is clearly in A.P.
first term ( a ) = 407
common difference ( d ) = 11
an = 693
a + ( n - 1 )d = 693
407 + ( n - 1 ) 11 = 693
divide each term with 11 , we get
37 + n - 1 = 63
n = 63 - 36
n = 27
I hope this helps you.
: )
Answered by
5
The numbers divisible by 9:
Ranging from 400-700
405, 414, 423, 432,441, 423, 432, ....... There are a total of 32 numbers from 400-700 which are divisible by the number 9.
This question is that of AP( Arithmetic Progression)
( a ) = 405, i.e. the 1st term
( d ) = a2 - a1 i.e. common difference
step 1:
Finding the d = 414 - 405 = 9
next step is that of finding the concerned term
let number of terms = n
If; (a)(n) = 693
a + ( n - 1 )(d) = 693 (693 being the last number which can be divisible, in the entire list)
405 + ( n - 1 )(9) = 693
45 + n - 1 = 77
n = 77 - 44
n = 33
Thanks for asking. I hope you like the answer and it helps you out.
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