Question

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Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

GRAPH IN NEXT POST

Answer 1

an = 8(one half)n − 2; average rate of change is −6

an = 10(one half)n − 2; average rate of change is 6

an = 8(one half)n − 2; average rate of change is 6

an = 10(one half)n − 2; average rate of change is −6

Answer 2

@SolomonZelman

Answer 3

@mathmate

Answer 4

@mathmale @mathmate

Answer 5

@zepdrix, can you help?
@mathmate, can you help?

Answer 6

So the common ratio is 1/2.
See how each term is getting cut in half each time?

\[\Large\rm a_n=a_1\left(\frac{1}{2}\right)^{n-1}\]What about the first term?

Answer 7

Oh they have a -2 in there >.< lemme fix that.

Answer 8

Haha no worries!!

Answer 9

I'll keep looking at it though, the -2 is throwing my brain off.

Answer 10

That's okay, honestly, if you could just give me the equation I could probably figure it out.

Answer 11

Ok ok ok I see what they did there.
That was confusing.
The -2 is part of the exponent.

Answer 12

So we start with our general for the geometric sequence:\[\Large\rm a_n=a_1\left(\frac{1}{2}\right)^{n-1}\]

Answer 13

You know what, you're right, I am so so sorry I wasn't more clear about that. I should have put ^n-2 or something!

Answer 14

They're giving us coordinates in the form of: \(\Large\rm (n,~a_n)\)
So we'll plug in the point \(\Large\rm (2,8)\) and solve for a_1 our first term.

Answer 15

\[\Large\rm 8=a_1\left(\frac{1}{2}\right)^{2-1}\]

Answer 16

So what do you get for your first term?

Answer 17

Understand how to solve for \(\Large\rm a_1\) in that equation? :o

Answer 18

Does a=16???

Answer 19

Ok very good. Let's plug that into our function:\[\Large\rm a_n=16\left(\frac{1}{2}\right)^{n-1}\]So this is where things get weird.
Maybe they wanted us to approach this differently.. I dunno.
But anyway, see how the exponent is supposed to be n-2?
So we need to take a 1/2 out of that whole thing.