Question

Which statements are true regarding the sequence below? Check all that apply.

Answer 1

Answer: A. It can be represented using the formula  $f(x+1)=\frac{6}{5}(f(x))$ when f(1)=$\frac{10}{3}$

C. It can be represented using the formula $f(x)=\frac{10}{3}[\frac{6}{5}]^{x-1}$

Step-by-step explanation:

We know that domain for every sequence is all natural numbers and range of the sequence is all real numbers.[thus D and E are wrong]

In A. the given formula is

$f(x+1)=\frac{6}{5}(f(x))$ when f(1)=$\frac{10}{3}$ such that

$f(2)=\frac{6}{5}(f(1))=\frac{6}{5}\times\frac{10}{3}=4$

$f(3)=\frac{6}{5}(f(2))=\frac{6}{5}\times4=\frac{24}{5}$

$f(4)=\frac{6}{5}(f(3))=\frac{6}{5}\times\frac{24}{5}=\frac{144}{25}$

∴ It represents the above sequence.

In B. given formula is $f(x)=4[\frac{6}{5}]^x$ such that

$f(1)=4[\frac{6}{5}]^1=\frac{24}{5}\neq\frac{10}{3}$

∴ It does not represent the above sequence.

In C. given formula is $f(x)=\frac{10}{3}[\frac{6}{5}]^{x-1}$ such that

$f(1)=\frac{10}{3}[\frac{6}{5}]^{1-1}=\frac{10}{3}$

$f(2)=\frac{10}{3}[\frac{6}{5}]^{2-1}=4$

$f(3)=\frac{10}{3}[\frac{6}{5}]^{3-1}=\frac{24}{5}$

$f(4)=\frac{10}{3}[\frac{6}{5}]^{4-1}=\frac{144}{25}$

∴ It represents the above sequence.

Answer 2

The answers are A and C