Pattern is the rule that guides the formation of a set.
- <em>The sequence of the first five mosaics is 5, 8, 11, 14, 17</em>
- <em>The sequence is arithmetic</em>
- <em>There are 32 tiles in the tenth mosaic.</em>
From the given design, the number of tiles used is:
![T_1 = 5](https://tex.z-dn.net/?f=T_1%20%3D%205)
![T_2 = 8](https://tex.z-dn.net/?f=T_2%20%3D%208)
![T_3 = 11](https://tex.z-dn.net/?f=T_3%20%3D%2011)
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<u>(a) The first five</u>
Notice that the difference in the number of tiles of successive mosaic is 3.
This means that:
![T_4 = T_3 + 3 = 11 +3 = 14](https://tex.z-dn.net/?f=T_4%20%3D%20T_3%20%2B%203%20%3D%2011%20%2B3%20%3D%2014)
![T_5 = T_4 + 3 = 14 +3 = 17](https://tex.z-dn.net/?f=T_5%20%3D%20T_4%20%2B%203%20%3D%2014%20%2B3%20%3D%2017)
So, the sequence of the first five mosaics is 5, 8, 11, 14, 17
<u>(b) The type of sequence</u>
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
<u>(c) The number of tiles in the tenth mosaic</u>
The nth term of an arithmetic sequence is:
![T_n = T_1 + (n - 1) \times d](https://tex.z-dn.net/?f=T_n%20%3D%20T_1%20%2B%20%28n%20-%201%29%20%5Ctimes%20d)
In this case:
![T_1 = 5](https://tex.z-dn.net/?f=T_1%20%3D%205)
![d =3](https://tex.z-dn.net/?f=d%20%3D3)
![n = 10](https://tex.z-dn.net/?f=n%20%3D%2010)
So, we have:
![T_{10} = 5 + (10 - 1) \times 3](https://tex.z-dn.net/?f=T_%7B10%7D%20%3D%205%20%2B%20%2810%20-%201%29%20%5Ctimes%203)
![T_{10} = 5 + 9 \times 3](https://tex.z-dn.net/?f=T_%7B10%7D%20%3D%205%20%2B%209%20%5Ctimes%203)
![T_{10} = 5 + 27](https://tex.z-dn.net/?f=T_%7B10%7D%20%3D%205%20%2B%2027)
![T_{10} = 32](https://tex.z-dn.net/?f=T_%7B10%7D%20%3D%2032)
There are 32 tiles in the tenth mosaic.
Read more about arithmetic sequence at:
brainly.com/question/18109692