Question

Find the number of integers between 100 and 1000
1) divisible by 7
2) not divisible by 7

Answer 1

105,112,119,………………..994

Here a (first term)=105

d (common difference)=7

an (last term)=994

an=a+(n-1)d

994=105+(n-1)7

994=105+7n-7

994=98+7n

994-98=7n

896=7n

n=896÷7

n=128

There are 128 numbers in between 100 and 1000 which are divisible by 7.

Total number between 100 and 1000 is 899
Hence the total numbers between 100 and 1000 which are not divisible by 7 will be
899-128=771

Answer 2

Divisible by 7

994=105+7x-7
7x=896
x=128

Not divisible by 7

Terms=1000-100+1= 901

Not divisible= 901-128= 773