Question

Which of the following represents the general equation for the geometric sequence? -1, -2, -4, ... an = 1 · 2n - 1 an = -2n - 1 an = 2n - 1 an = 1 · 2n + 1

Answer 1

-1,-2,-4

an = a1 * r^(n - 1)
a1 = first term = -1
r = common ratio = 2

so the equation would be : an = -1 * 2^(n - 1)

Answer 2

Answer:

$a_{n} = - 2^{n-1}$.

Step-by-step explanation:

Given : geometric sequence  -1, -2, -4, ...

To find : Which of the following represents the general equation for the geometric sequence.

Solution : We have given

Geometric sequence  -1, -2, -4, ...

By the formula for general equation : $a_{n} = a_{1} *r^{n-1}$.

Where,   $a_{n}$ = last term.

$a_{1}$ =  first term.

r = common ratio.

r ( common ratio ) = $\frac{second\term}{first\term}$.

In  -1, -2, -4, ...

$a_{1}$ = -1.

r ( common ratio ) = $\frac{-2}{-1}$.

r ( common ratio ) =2.

Plug the values in formula

$a_{n} = (-1) * 2^{n-1}$.

$a_{n} = - 2^{n-1}$.

Therefore,  $a_{n} = - 2^{n-1}$.