👤

Answer :

Thisbis a general geometric progression

  • first term=a=9
  • common ratio=2/3=r

So iterative formula

  • ar^{n-1}
  • 9(2/3)^{n-1}
Semsee45go

Answer:

[tex]a_n=9 \cdot \left(\frac{2}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}a_1=9\\a_n=\frac{2}{3}(a_n-1)\end{cases}[/tex]

General form of a geometric sequence:

[tex]a_n=ar^{n-1}[/tex]

where:

  • a is the first term
  • r is the common ratio

Therefore:

  • [tex]a = a_1 = 9[/tex]
  • [tex]r = \dfrac{2}{3}[/tex]

Substitute the given values into the general formula:

[tex]\implies a_n=9 \cdot \left(\frac{2}{3}\right)^{n-1}[/tex]

Learn more at:

https://brainly.com/question/27783194

Go Teaching: Other Questions