Question

23. How many positive integers between 100 and 999 inclusive a) are divisible by 7? B) are odd? C) have the same three decimal digits? D) are not divisible by 4? E) are divisible by 3 or 4? F ) are not divisible by either 3 or 4? G) are divisible by 3 but not by 4? H) are divisible by 3 and 4?

Answer 1

a) Use the formula for series

A=a+(n-1)d

d=common difference

A=last term

n=no. Of terms

a=first term

Now a=105,d=7,A=994

THEREFORE

994=105+(n-1)7

We get n=128.

HOPE THIS HELPZZ

NAZ:):)

THANK U

Answer 2

Sum of the First n Natural Numbers. We prove the formula 1+ 2+ ... + n = n(n+1) / 2, for n a natural number