Numbers are arranged in a line as follows.
1/1, 1/2, 2/2, 1/3, 2/3, 3/3, 1/4, 2/4, 3/4, 4/4, 1/5, 2/5, -----
Answer the following questions.
(1) Find the 26th number.
(2) Find the sum total of the numbers from the 37th to the 55th.
(3) The sum total was 76 when I added numbers sequentially from the beginning.
Which number did I add by ?
Answer
(1) 5/7
(2) 10.5
(3) 136th
Solution
(1)
| Group | 1st | 2nd | 3rd | 4th | 5th |
| 1/1 | 1/2, 2/2 | 1/3, 2/3, 3/3 | 1/4, 2/4, 3/4, 4/4 | 1/5, 2/5, -- |
1 + 2 + 3 + 4 + 5 + 6 = 21
Since the 26th number is 5th number in seventh group starting from 1/7, it is 5/7.
(2)
1 + 2 + 3 + 4 + 5 + 6 +7 + 8 = 36
37th = 1/9
55th = 10/10
1/9 + 2/9 + ------+ 9/9 + 1/10 + 2/10 + ----- + 10/10
= 45/9 + 55/10 = 10.5
(3)
Sum of 1st group = 1
2nd group = 1.5
3rd group = 2
4th group = 2.5
5th group = 3
According to 1 + 2 + 3 + 4 + 5 + 6 +7 + 8 = 36, 76 - 36 = 40.
Then it is estimated that 1.5 + 2.5 + 3.5 + 4.5 + 5.5 + 6.5 + 7.5 + 8.5 = 40 and it is 40.
8.5 is sum of 16th group.
(1+16) × 16 / 2 = 136th
