Question

Which function forms a geometric sequence when x = 1, 2, 3, . . . ?

Answer 1

Answer:

$a) f(x)=3(4)^{x}$

Step-by-step explanation:

The correct options are:

$a) f(x)=3(4)^{x}$

$b) f(x)=3(x)^{2}$

$c) f(x)=2x+4$

$d) f(x)=x+(2)^{4}$

We have to identify which of these options will form a geometric sequence. A geometric sequence is defined as the sequence in which the ratio of two consecutive terms remain the same. This ratio is known as common ratio of the sequence. General term of a geometric sequence is defined as:

$a_{n}=a_{1}(r)^{n-1}$

Here,

$a_{n}$ is the nth term of the sequence. Replacing n by different values will give us the term of the sequence at that values.

The option resembling the general term of the geometric sequence is option a, with only difference that in place on "n", the variable x is used in the option. So option a should be our answer. Lets verify this.

$f(x)=3(4)^{x}$

For x = 1, the value will be:

f(1) = 12

For x = 2, the value will be:

f(2) = 48

For x =3, the value will be:

f(3) = 192

The ratio of these terms is:

Ratio of f(2) and f(1) = 4

Ratio of f(3) and f(2) = 4

Therefore, the function given in option a represents a geometric sequence.