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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.

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meerkat18

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 

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

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