Question

Hi, I am confused on this question:

The sequence 12, 15, 18, 21, 51, 81, ... consists of all positive multiples of 3 that contain at least one digit that is a 1. What is the 50th term of the sequence?


(Source: 2006 National Target #5)

Answer 1

321.

Explanation:

The next term after 81 is 102 .

Between 102 and 198 inclusive we have (198-102) / 5 + 1 = 96/3 + 1 = 33 terms - these will all have at least one 1 and be divisible by 3.

So 198 = 6 + 33 = 39th term.

After 198 we have 201, 210, 213, 219, 231, 261, 291, 312, 315, 318, 321

The answer is 321..