Question

consider the sequence 16,-8,4,-2,1,
A. describe the pattern formed in the sequence.
B. find the next three terms

Answer 1

please help me please

Answer 2

A geometric sequence with first term 16 and common ratio = 0.5

Answer 3

do you see a pattern?

Answer 4

I meant r = -0.5
My bad

Answer 5

ugh no because i see it go from negative numbers to positive can you exsplain everything to me please?

Answer 6

Ok... A geometric sequence is such a sequence that each term is the previous term multiplied by some constant known as the common ratio.

In this case, can you work out the common ratio?

Answer 7

okay let me see if i see one but yeah i know what a sequence is but like when it jumps from negative to positive im like lost

Answer 8

Well, forget about that, for the moment...
What's -8/16
?

Answer 9

\[\LARGE \text{common ratio} = \frac{\text{second term}}{\text{first term}}\]

Answer 10

^I'd just like to add that that thing you said only applies if we're sure we're dealing with a geometric sequence :)

Answer 11

-0.5

Answer 12

That's right. Now what's 4/-8? what's -2/4? 1/-2?

Answer 13

oh i get it now so thats the sequence right it you get your number if you divide that by the number right?

Answer 14

You'll notice that each term is the previous term multiplied by -0.5... right?
You do notice that, right? :)

Answer 15

yeah okay now for the secound part

Answer 16

Ok, with that established, what do you think comes after 1?

Answer 17

okay so 1 / -0.5 right?

Answer 18

No... 1 * -0.5
We established that each term is the previous term MULTIPLIED by -0.5, the common ratio.

Try again :)

Answer 19

oh crap my bad i was looking at my next question okay so 1 times -0.5 = -0.5 right

Answer 20

That's right. What comes after -0.5, then? :)

Answer 21

by the way, I think this problem wants fractions, not decimals, you might do well to put
-(1/2) instead of -0.5

Answer 22

so you still times it right? if so its -1

Answer 23

No... what's -0.5 x -0.5?
I'm pretty sure it's not -1

Answer 24

try
\[-\frac{1}{2}\times-\frac{1}{2}\]

Answer 25

oh no i got it wrong hold on

Answer 26

0.25?

Answer 27

that's right 0.25, or
1/4
Now, finally, what comes after that?

Answer 28

1/4 times -1/2 right?

Answer 29

that's right :)

Answer 30

okay

Answer 31

So what did you get?

Answer 32

-0.345

Answer 33

really?
try it again, make sure

Answer 34

0.125?

Answer 35

Wait a sec, your 0.125, are you sure it's positive?

Answer 36

no its negative

Answer 37

watch your signs ... >.>
Anyway, now you have your next three terms :)

Answer 38

thax you :)

Answer 39

To sum it all up, the sequence has the form :
\[x_{n}=16\left( -\frac{1}{2} \right)^{n-1} = (-1)^{n+1}(16)(0.5)^{n-1}\]

Answer 40

Where
\[x_{n} \]
is the nth term in the sequence