Hints and solutions to Look for a pattern #4

In each table, fill in the missing numbers or expressions:

• (a)

  1	2	3	4	5	8	10	?
  3	6	9	12	?	?	?	48

  • The numbers in the bottom row are three times their counterparts in the top row. So the filled in table looks like this:

    1	2	3	4	5	8	10	16
    3	6	9	12	15	24	30	48

• (b)

  1	2	3	4	5	9	12	?
  3	5	7	9	?	?	?	37

  • For this one, the rule is multiply by 2 and add one to go from the top to the bottom row. So the filled-in table looks like this:

    1	2	3	4	5	9	12	18
    3	5	7	9	11	19	25	37

• (c)

  1	2	3	4	5	8	?
  1/2	1/6	1/12	1/20	?	?	1/110

  • Last but certainly not least, all the numerators in the bottom are 1, and the denominators are the product of the number in the top row with the number that comes after it (2 = 1 times 2, 6 = 2 times 3, etc). So the filled-in table is like this:

    1	2	3	4	5	8	10
    1/2	1/6	1/12	1/20	1/30	1/72	1/110