Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 −4
2 20
3 −100

Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n	an
1	−4
2	20
3	−100

anonymous · Answer

@kc_kennylau

kc_kennylau · Answer

What's the common ratio?

shamil98 · Answer

$$\huge x_n = ar^{n-1}$$

shamil98 · Answer

a = first term
r = ratio
n = number of terms

anonymous · Answer

pls teach me how to figure out the common ratio @kc_kennylau

kc_kennylau · Answer

$$\Large r=a_2\div a_1$$

shamil98 · Answer

so what is 
$$20 \div -4$$?

solomonzelman · Answer

$$r=a_{n} \div a_{n-1}$$

kc_kennylau · Answer

@shamil98 @woohoo sorry i got to go now :)

anonymous · Answer

ok so r=-100/-4

shamil98 · Answer

anyways you have:
n = 3
a = -4
r = -5
So using the formula i gave you, just plug them in

shamil98 · Answer

a_2 = 20
a_1 = -4

20 / - 4  = -5

anonymous · Answer

ohhhhh ok

anonymous · Answer

400?

shamil98 · Answer

$$\Huge x_n = ar^{n-1} $$
$$\large \text{You have the values for a,r, and n.}$$
$$\large \text {r = -5 , n = 3 , a = -4}$$
$$\large \text{So,now, just plug them into the formula.}$$

shamil98 · Answer

Well, actually, it says create the formula for it, so leave n just as n.

anonymous · Answer

an = −5(−4)n − 1 where n ≥ 1

shamil98 · Answer

Correct, i assume you mean to the power of n-1.
$$\large a_n = -5(-4)^{n-1}$$

anonymous · Answer

Thank You!

anonymous · Answer

isnt this one wrong? do you remember?

kc_kennylau · Answer

Why is this wrong?

anonymous · Answer

It was wrong when I tried.

solomonzelman · Answer

wait what ? what was wrong ?

anonymous · Answer

an = −5(−4)n − 1 where n ≥ 1
 the answer

anonymous · Answer

@SolomonZelman an = −5(−4)n − 1 where n ≥ 1 

an = −4(−5)n − 1 where n ≥ 1 

an = −4(5)n − 1 where n ≥ −4 

an = 5(−4)n − 1 where n ≥ −4 
 those are the answers wouldn't it be the last one

solomonzelman · Answer

answers for what question ?

anonymous · Answer

this one

solomonzelman · Answer

these are the options you posted just now, and the question ?

anonymous · Answer

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n	an
1	−4
2	20
3	−100
 woohoo's original question.

solomonzelman · Answer

I don't even know what to say... I am just going to say that the question says 
"Given a geometric sequence in the table below $\normalsize\color{red}{ \bf     in ~the~ table~below	 }$."

anonymous · Answer

an = 5(−4)n − 1 where n ≥ −4 was wrong...hm...I have no idea what the right answer was.

anonymous · Answer

It's the second option that xoalybabyxo posted.