Question

Which statements are true regarding the sequence below? Check all that apply.
$\frac{10}{3}$, $4$, $\frac{24}{5}$, $\frac{144}{25}$, ...
A. It can be represented using the formula $f (x+1) = \frac{6}{5}(f(x))$ when $f(1)= \frac{10}{3}$.
B. It can be represented using the formula $f(x)=4[\frac{6}{5}] ^{x}$.
C. It can be represented using the formula $f(x)= \frac{10}{3} [\frac{6}{5}] ^{x-1}$
D. The domain of the sequence is all real numbers.
E. The range of the sequence is all natural numbers.

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

Out of the given 5 statements, only statements f(x+1)=6/5f(x) and f(x)=4(6/5)^x are true regarding the given sequence while the rest of the options are wrong.

The given sequence is:

$\frac{10}{3},4,\frac{24}{5},\frac{144}{5},....$

What is a sequence?

A sequence is a collection of objects in which repetitions are allowed and order is important.

A)$f(x+1)=\frac{6}{5} f(x)$

If we put x=1,2,3.....considering f(1)=10/3

We get the same sequence $\frac{10}{3},4,\frac{24}{5},\frac{144}{5},....$

So, option A is correct.

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

If we put x=1,2,3.....

We get the same sequence $\frac{10}{3},4,\frac{24}{5},\frac{144}{5},....$

So, option C is also correct.

Options D & E are incorrect because the domain of a sequence is a set of natural numbers while the range is the set of real numbers.

Thus, statements A and C are true regarding the given sequence.

To get more about sequences visit:

https://brainly.com/question/1275192