Question

Which formula can be used to describe the sequence?

Answer 1

Answer:

The formula  that can be used to describe the given  sequence is $f(x)=-4(6)^{x-1}$

Step-by-step explanation:

Given : sequence -4,  −24, −144,...

We have to find the formula that can be used to describe the given sequence  -4,  −24, −144,...

A geometric sequence is a sequence in which each higher term is multiplied by a constant number called common ratio.

Written as a, ar , ar², ar³., ....

and general term is calculated as $a_n=ar^{n-1}$

Where a is first term and r is common ratio.

Consider the given sequence  -4,  −24, −144,...

We find the common ratio ,

$a=-4, \\\\ar=-24,\\\\\ ar^2=-144$

Thus, common ratio is given as $r=\frac{ar}{r}=\frac{-24}{-4}=6$

Thus, the given sequence is a geometric sequence.

The general term is given by $a_n=ar^{n-1}$

Put a = -4 , r = 6

We have

$a_n=-4(6)^{n-1}$

Thus, the formula  that can be used to describe the given  sequence is $f(x)=-4(6)^{x-1}$

Answer 2

Answer:

$f(x) = -4(6)^{x-1}$

Step-by-step explanation:

Given sequence,

-4, -24, -144, .....

Since,

$\frac{-24}{-4}=\frac{-144}{-24}=.........=6$

Thus, the given sequence is the Geometric sequence having common ratio 6,

Since, the formula of nth term of a GP is,

$a_n = ar^{n-1}$

Here, a = -4 ( first term ) and r = 6 ( common difference,

Let x represents the total number of terms,

And, f(x) represents the xth term,

Then the required formula would be,

$f(x) = -4(6)^{x-1}$