Since a train stops at the station every 12 minutes, the times at which a train stops at the station form an arithmetic sequence with common difference 0:12. Also, because the first train stops at 6:00A.M., the first term of the sequence is 6:00. Let's write some terms of the sequence.
a_1
6:00
a_2
6:00+ 0:12=6:12
a_3
6:12+ 0:12=6:24
a_4
6:24+ 0:12=6:36
a_5
6:36+ 0:12=6:48
a_6
6:48+ 0:12=7:00
a_7
7:00+ 0:12=7:12
a_8
7:12+ 0:12=7:24
a_9
7:24+ 0:12=7:36
We see in our table that the next train after 7:29A.M. stops at 7:36A.M. Let's find out how many minutes we need to wait.
7:36A.M. - 7:29A.M. = 7minutes
Therefore, we need to wait 7 minutes.
Extra
Note that in this case, we wrote some terms of the arithmetic sequence instead of using its formula. The reason is that it could be difficult to multiply and add time instead of numbers. However, if special attention is paid and calculations are done very carefully, it is possible to find the answer by using the explicit formula.
