Question

Reuben learned in art class that a mosaic is made by arranging small pieces of colored material such as glass or tile to create a design. Reuben created a mosaic using tiles. Then he decided on a growing pattern and created the second and third mosaics.
a. For the first five mosaics, write the sequence that is formed by the number of tiles in each mosaic.
b. Is this sequence arithmetic, geometric, or neither? How do you know?
c. How many tiles will be in the tenth mosaic? How do you know?

Answer 1

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:

$T_1 = 5$

$T_2 = 8$

$T_3 = 11$

(a) The first five

Notice that the difference in the number of tiles of successive mosaic is 3.

This means that:

$T_4 = T_3 + 3 = 11 +3 = 14$

$T_5 = T_4 + 3 = 14 +3 = 17$

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:

$T_n = T_1 + (n - 1) \times d$

In this case:

$T_1 = 5$

$d =3$

$n = 10$

So, we have:

$T_{10} = 5 + (10 - 1) \times 3$

$T_{10} = 5 + 9 \times 3$

$T_{10} = 5 + 27$

$T_{10} = 32$

There are 32 tiles in the tenth mosaic.

Read more about arithmetic sequence at:

brainly.com/question/18109692