Question

I am NOT looking for answers, I just need help and a walkthrough of everything because I am totally confused.

The development studio behind the newest video game, Super Ostrich Racers, needs your help. Super Ostrich Racers is an exciting, fast-paced adventure game where your ostrich runs through twenty different levels while collecting coins. They need you to develop the number of coins and points for each level and provide data for the programming team.

Anybody good with geometric sequences???

Answer 1

This is under geometric sequences/ series, correct?

Answer 2

Yes, it is.

Answer 3

so an easy way to do this one is to make the points in the level a geometric sequence. Then, the sum of the points will be part of a geometric series...

Answer 4

Instructions:
create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0.
Provide reasons and justification of how you know the Coins sequence you created is arithmetic and how you know the Points sequence is geometric.

then it gives me a table:

Levels Coins? Levels Points?


1 1
2 2
3 3

I need help first starting, I'm so confused. Math isn't my thing:/

Answer 5

This probably really just wants to make you do two things: make an arithmetic sequence and make a geometric sequence. Do you know what those are?

Answer 6

arithmetic is the difference between each term so you would add the value each time and geometric is where you multiply? Or something like that?

Answer 7

Yes. In an arithmetic sequence, for each succeeding number you add a common difference. In a geometric sequence, for each succeeding number you multiply by a common ratio. because we need positive coins and positive points, let's go with a positive common ratio and a positive common difference.

Answer 8

so I just choose a number and go from there?

Answer 9

Yeah. For the arithmetic sequence make sure the common difference is greater than one. For the geometric sequence I would HIGHLY suggest using a common ratio of 2, because geometric sequences grow VERY quickly.

Answer 10

okay so for the arithmetic sequence i'll use 4, and for geometric ill use 2.

Answer 11

as for the reasons, simply state that the definition of an arithmetic sequence is that it has a starting number and a common difference, and then state the common difference that you have. for the geometric sequence state the starting number and the common ratio.

Answer 12

sooo for geometric it would be 2,4,6,8? And arithmetic would be like 4,8,12,16? Or am I just totally off?

Answer 13

no. you got the arithmetic right, but for geometric you multiply. so it might look like 2 4 8 16 32, etc

Answer 14

oooooh ok. I got you now

Answer 15

SO I would enter those values in the table?

Answer 16

yeah, basically.

Answer 17

Ok it only gives me three spaces for coins and points. Coins are arithmetic and points are geometric. SO I guess I'll just put the first three numbers of each sequence for the coins and points...

Answer 18

yeah, go ahead

Answer 19

now it says demonstrate how a recursive process will allow you to find the number of coins and points on all levels up to level 5.

Answer 20

I'm guessing 5 would be multiplied by something ?

Answer 21

no - recursive just means that you use the previous number to find the next number. so for geometric you just continue to multiply by your common ratio, while for arithmetic you continue to add by your common ratio.

Answer 22

so just add two numbers to what I already have. 4,8,12,16,20 & 2,4,8,16,32

Answer 23

it now asks me to create the sequence formulas, an, for the coins and the points based on the level in the game. Then describe how the formula can be used to find the coins and values on level 15 using complete sentences.

Answer 24

i appreciate your help, im almost done!

Answer 25

for the arithmetic sequence formulas, just use \(\large a_n=a_1+(n-1)d\)
where n is the value you want (in this case 15 because of level 15)
d is the common difference (I believe you used 4)
and\(a_1\) is your first value, in this case 4.

as for the geometric sequence formulas, just use \(\huge 2^n\) where n is the value of your level.

Answer 26

what's n?

Answer 27

nevermind, I see

Answer 28

a15=4=(15-1) (4) ?

Answer 29

a15=72 ?

Answer 30

I think so.

Answer 31

no, i got 60 actually.

Answer 32

then 2^15? Which is a big number, like 32,768..

Answer 33

How did you get 60?

Answer 34

Wait! I got it. I calculated it wrong

Answer 35

If the game only has 20 levels, explain how to find the value of the series for the coins and the points. Use complete sentences and arrive at final values.

I'm guessing you would do the same thing here, just use 20 right?

Answer 36

yeah, I think so.

Answer 37

and do you know how I would find the domain/range of the sequences?