There are sequences P and Q arranged according to a certain rule.
P 3, 9, 27, 81,-----
Q 2, 4, 6, 8, 10,-----
Two sequences P and Q are matched to make a sequence R in a small order.
R 2, 3, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22,-------
Answer the following questions on the sequence R.
(1) Which number is 30?
(2) Which number is 300?
(3) Find the 81st number.
(4) Find the 2014th number.
Answer
(1) 18th
(2) 155th
(3) 154
(4) 4014
Solution
(1) 30 is the number of the sequence Q and is 30 / 2 = the 15th number.
Because there are three numbers of 3, 9, 27 of the sequence P until 30, 30 is 15 + 3 = the 18th number.
(2) The sequence of P is 3, 9, 27, 81, 243, 729, 2187, 4374----.
300 is the number of the sequence Q and is 300 / 2 = the 150th number.
Because there are five numbers of 3, 9, 27, 81, 243 of the sequence P until 150, 150 is 150 + 5 = the 155th number.
(3) The 81st number of Q is 81 × 2 = 162.
There are 4 numbers of P until 162. 81 - 4 = the 77th number is 77 × 2 = 154.
(4) The 2014th number of Q is 2014 × 2 = 4028.
There are 7 numbers of P until 4028.
2014 - 7 = the 2007th number is 2007 × 2 = 4014.
