Question

The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the geometric sequence 1, -2, 4, -8, ...? an = 1 · (-2)n - 1 an = -2 · 1n - 1 an = -8 · (-2)n - 1 an = 1 · 2n - 1

Answer 1

Answer:

$\huge\boxed{a_n=1\cdot(-2)^{n-1}}$

Step-by-step explanation:

$a_n=a_1r^{n-1}$

We have the geometric sequence: 1, -2, 4, -8, ...

Find the common ratio:

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

$a_1=1,\ a_2=-2$

substitute:

$r=\dfrac{-2}{1}=-2$

Substitute

$a_1=1;\ r=-1$

to

$a_n=a_1r^{n-1}$

$a_n=1\cdot(-2)^{n-1}$

Answer 2

Answer:

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

Step-by-step explanation:

Hi there!

Let's do it,

1)$1,-2,4,-8$  

First let's find the q, the common ratio by dividing the second term by the anterior one.

-2:1 =-2

4:-2=-2

So the common ratio is -2. Plugging in on the General formula:

$a_{n}=a_{1}q^{n-1}$

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