Question

Given the functions f(n) = 11 and g(n) = (three over four)n − 1, combine them to create a geometric sequence, an, and solve for the 9th term.

Answer 1

Solution:

The two function given are :

f(n) = 11, g(n) = $[\frac{3}{4}]^{n-1}$

We have to form a geometric sequence by combining f(n) and g(n).

So, the sequence having nth term is ,$a_{n}$ = f(n) × g(n)

                                                        = 11 ×  $[\frac{3}{4}]^{n-1}$

Starting from , n=1,2,3,4,5,.......

First term is given by = $a_{1}=11 \times (\frac{3}{4})^{1-1}=11 \times (\frac{3}{4})^{0}=11$

Common ratio = $\frac{3}{4}$=(Second Term )÷ (First Term)

9 th Term = $11 \times [\frac{3}{4}]^{9-1}=11 \times (\frac{3}{4})^{8}$

Answer 2

The question is asking to calculate and combine the said function to create a geometric sequence, and solve for the 9th term, base on my further calculation, the possible answer would be  an = 11(three fourths)n − 1; a9 ≈ 1.101, I hope you are satisfied with my answer and feel free to ask for more