Question

how many 3 digit numbers are there in which are divisible by 6 & solve it by giving explaination

Answer 1

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

 a + (n - 1)d = 996

 102 + (n - 1) x 6 = 996

 6 x (n - 1) = 894

 (n - 1) = 149

 n = 150

 Number of terms = 150.

Answer 2

every 6th no. is divisible by 6. so, starting from 100 to 999 the first no. divisible by 6 is 102
then next is 102+6 i.e. 108 and so on till 996. now, use sequence and series
a=102 the first term
b=996 the last term
d=6 interval
b=a+(n-1)d; n is the answer
solve it to get the answer