Pattern is the rule that guides the formation of a set.
- The sequence of the first five mosaics is 5, 8, 11, 14, 17
- The sequence is arithmetic
- There are 32 tiles in the tenth mosaic.
From the given design, the number of tiles used is:
[tex]T_1 = 5[/tex]
[tex]T_2 = 8[/tex]
[tex]T_3 = 11[/tex]
(a) The first five
Notice that the difference in the number of tiles of successive mosaic is 3.
This means that:
[tex]T_4 = T_3 + 3 = 11 +3 = 14[/tex]
[tex]T_5 = T_4 + 3 = 14 +3 = 17[/tex]
So, the sequence of the first five mosaics is 5, 8, 11, 14, 17
(b) The type of sequence
The sequence is arithmetic
This is so, because the difference in the number of tiles of successive mosaic is 3.
This difference is called the common difference
(c) The number of tiles in the tenth mosaic
The nth term of an arithmetic sequence is:
[tex]T_n = T_1 + (n - 1) \times d[/tex]
In this case:
[tex]T_1 = 5[/tex]
[tex]d =3[/tex]
[tex]n = 10[/tex]
So, we have:
[tex]T_{10} = 5 + (10 - 1) \times 3[/tex]
[tex]T_{10} = 5 + 9 \times 3[/tex]
[tex]T_{10} = 5 + 27[/tex]
[tex]T_{10} = 32[/tex]
There are 32 tiles in the tenth mosaic.
Read more about arithmetic sequence at:
https://brainly.com/question/18109692
