Question

a) Write a sequence to represent how many shaded triangles there are at each stage.b) Based on this sequence, write a formula for the nth term of the sequence.c) Using at least two sentences, describe what is represented by each term in the sequence.

Answer 1

Given:

The objective is,

a) To write a sequence to represent the number of shaded triangles.

b) To write the nth term of the sequence

c) To describe the sequence.

a)

The sequnce of the shaded triangles is,

`s=1,\text{ 3, 9}\ldots\ldots`

Hence, the sequence to represent the number of shaded triangles is obtained.

b)

The nth term of the sequence can be calculated as,

`\begin{gathered} T_n=a\cdot r^(n-1) \\ T_n=1\cdot3^(n-1) \\ T_n=3^(n-1) \end{gathered}`

Hence, the formula for nth term of the sequence is obtained.

c)

Compare the ratio of the sequence.

`\begin{gathered} r=\frac{\sec ond\text{ term}}{first\text{ term}} \\ r=(3)/(1) \\ r=3 \end{gathered}`

Similarly,

`\begin{gathered} r=\frac{third\text{ term}}{\sec ond\text{ term}} \\ r=(9)/(3) \\ r=3 \end{gathered}`

Since the ratios of each term of the sequence is equal, the given sequence is a geometric progression.

Hence, the representation of each term of the sequence is described.