Question

how many two digit number is divisible by 3 and arithmetic progression

Answer 1

Let two digit numbers are 10, 11, 12 , -------------99

which are divisible by 3 are 12, 15 ...............,99.

Here a = 12 and common dofference = 3 , an = l = 99

nth term (tn) = a + ( n - 1) d

⇒ 99 = 12 + ( n - 1) 3

⇒ (n - 1)3 = 99 - 12 = 87

⇒ ( n -1) = 87 / 3

⇒ n - 1 = 29

∴ n = 30

∴  30 two digit numbers which are divisible by 3.