The nth term of a sequence by sdfwerte

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									                Number patterns
When we are given a number pattern, we can
see it more clearly if we arrange it in a table:




       3,        5,         7,        9,       11
                   Number patterns
   When we are given a number pattern, we can
   see it more clearly if we arrange it in a table:

 red
           1         2         3         4            5
tiles
blue
           3         5         7         9        11
tiles
                  Number patterns
   Then we look at the number pattern and see
   how much it increases/decreases each time:

 red
          1        2        3        4          5
tiles
blue
          3        5        7        9          11
tiles
                  Number patterns
   Then we look at the number pattern and see
   how much it increases/decreases each time:

 red
          1        2        3        4          5
tiles
blue
          3        5        7        9          11
tiles

              2
                  Number patterns
   Then we look at the number pattern and see
   how much it increases/decreases each time:

 red
          1        2        3        4          5
tiles
blue
          3        5        7        9          11
tiles

              2        2
                  Number patterns
   Then we look at the number pattern and see
   how much it increases/decreases each time:

 red
          1        2        3        4          5
tiles
blue
          3        5        7        9          11
tiles

              2        2        2         2
                     Number patterns
   This number gives us the first part of our
   formula:

 red
          1           2            3       4       5
tiles
blue
          3           5            7       9       11
tiles

                 2        2            2       2

  blue tiles =       x red tiles
                     Number patterns
   This number gives us the first part of our
   formula:

 red
          1           2            3       4       5
tiles
blue
          3           5            7       9       11
tiles

                 2        2            2       2

  blue tiles =       x red tiles
                   Number patterns
   This number gives us the first part of our
   formula:

 red
          1         2            3       4       5
tiles
blue
          3         5            7       9       11
tiles

               2        2            2       2

  blue tiles = 2   x red tiles
                   Number patterns
   Then we test our formula to see if we get the
   correct number of blue tiles:

 red
          1         2            3     4           5
tiles
blue
          3         5            7     9           11
tiles



  blue tiles = 2   x red tiles
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles:

  red
           1         2            3     4           5
 tiles
2x red
blue
           3         5            7     9           11
tiles

   blue tiles = 2   x red tiles
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles:

  red
           1         2            3     4           5
 tiles
2x red     2         4            6     8           10
blue
           3         5            7     9           11
tiles

   blue tiles = 2   x red tiles
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles: We do not.
                    We must add 1 each time
  red
           1         2            3     4           5
 tiles
2x red     2         4            6     8           10
blue
           3         5            7     9           11
tiles

   blue tiles = 2   x red tiles
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles: We do not.
                    We must add 1 each time
  red
           1         2        3         4           5
 tiles
2x red     2         4        6         8           10
blue
           3         5        7         9           11
tiles
              So we must add one to the formula:
   blue tiles = 2 x red tiles
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles: We do not.
                    We must add 1 each time
  red
           1         2        3         4           5
 tiles
2x red     2         4        6         8           10
blue
           3         5        7         9           11
tiles
              So we must add one to the formula:
   blue tiles = 2 x red tiles + 1
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles:

  red
           1         2        3         4           5
 tiles
2x red     2         4        6         8           10
blue
           3         5        7         9           11
tiles
             Finally, we should check the formula:
   blue tiles = 2 x red tiles + 1
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles:

  red
           1         2          3       4           5
 tiles
2x red     2         4          6       8           10
blue
           3         5          7       9           11
tiles
             Finally, we should check the formula:
   blue tiles = 2 x red tiles + 1
For 5 red tiles = 2 x 5 + 1
                = 10 + 1 = 11
                    Number patterns
    Then we test our formula to see if we get the
    correct number of blue tiles:

  red
           1         2            3        4           5
 tiles
2x red     2         4            6        8        10
blue
           3         5            7        9        11
tiles

   blue tiles = 2   x red tiles       +1
For 5 red tiles = 2 x 5 + 1                correct !
                = 10 + 1 = 11
                    Number patterns
    So blue tiles = 2 x red tiles + 1
       is the formula for our number pattern

  red
           1         2            3        4           5
 tiles
2x red     2         4            6        8       10
blue
           3         5            7        9       11
tiles

   blue tiles = 2   x red tiles       +1
For 5 red tiles = 2 x 5 + 1                correct !
                = 10 + 1 = 11

								
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