GK 2017 Q21
21. Each number in the sequence starting 2, 3, 6, 8, 8, 4, ... is obtained in the following way. The first two numbers are 2 and 3 and afterwards each number is the last digit of the product of the two preceding numbers in the sequence. What is the 2017th number in the sequence?
- A 8
- B 6
- C 4
- D 3
- E 2
Grey Kangaroo 2017, Question 21. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 2
Continue the sequence as described to obtain 2, 3, 6, 8, 8, 4, 2, 8, 6, 8, 8, 4, 2, 8, 6, 8 and so on. Since the value of each term depends only on the preceding two terms, it can be seen that, after the first two terms, the sequence 6, 8, 8, 4, 2, 8 repeats for ever. Now 2017 − 2 = 335 × 6 + 5. Therefore the 2017th number in the sequence is the fifth number of the repeating sequence 6, 8, 8, 4, 2, 8. Hence the required number is 2.
Solution © UK Mathematics Trust, from the GK 2017 solutions.