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,
[tex]s=1,\text{ 3, 9}\ldots\ldots[/tex]
Hence, the sequence to represent the number of shaded triangles is obtained.
b)
The nth term of the sequence can be calculated as,
[tex]\begin{gathered} T_n=a\cdot r^{n-1} \\ T_n=1\cdot3^{n-1} \\ T_n=3^{n-1} \end{gathered}[/tex]
Hence, the formula for nth term of the sequence is obtained.
c)
Compare the ratio of the sequence.
[tex]\begin{gathered} r=\frac{\sec ond\text{ term}}{first\text{ term}} \\ r=\frac{3}{1} \\ r=3 \end{gathered}[/tex]
Similarly,
[tex]\begin{gathered} r=\frac{third\text{ term}}{\sec ond\text{ term}} \\ r=\frac{9}{3} \\ r=3 \end{gathered}[/tex]
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.
