Q25 of 176 Page 8

Find the number of all positive integers of 3 digits which are divisible by 5.

The list of 3 digit numbers divisible by 5 is:

100, 105, 110,…,995

Here a = 100, d = 105 – 100 = 5, a_n = 995

We know that

a_n = a + (n – 1)d

995 = 100 + (n – 1)5

⇒ 895 = (n – 1)5

⇒ 179 = n – 1

⇒ 180 = n

So, there are 180 three– digit numbers divisible by 5.

If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.

If t_n be the nth term of an A.P. such that find .

How many three digit numbers are divisible by 7.

If t_n denotes the nth term of an A.P., show that t_m + t_2n+m = 2 t_m+n.