Question

example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________his gym time by ____________. If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence.

Answer 1

@peachpi

Answer 2

Pick numbers for the 1st and 3rd blanks. For the second since it's geometric, you want it to be a multiplier so use a word like halves, doubles, triples, etc.

Answer 3

Wait no. You only need a number for the first blank. For the second it will still be increases/decreases. For the third use half, double, triple

Answer 4

Ok so Anthony goes to the gym for 30min everyday he increases his time by half an hour

Answer 5

Wait did that even make sense what I just said

Answer 6

He increases his time by half an hour

Answer 7

Increasing by half an hour would make it an arithmetic sequence because 30 minutes is a fixed amount. You can say he increases his time by double. So he'd do it for 30 minutes the first day, 60 the second, 120 the third and so on. The constant multiplier is what makes it geometric

Answer 8

Arithmetic (adding 30 everyday)
day 1 = 30
day 2 = 60
day 3 = 90
day 4 = 120

Geometric (doubling everyday)
day 1 = 30
day 2 = 60
day 3 = 120
day 4 = 240

Answer 9

does that make sense to you?

Answer 10

So your basically multiplying by 20

Answer 11

multiplying by 2

Answer 12

Oh yeah sorry that was dumb so that's all you do until you get the answer for day 5

Answer 13

Well yeah for day 5 it's going to be 480. Do they want to see you set up the geometric formula like you had to do for the last one?

Answer 14

Yes that's the part the I don't understand is how to set it up

Answer 15

\[a_n=a_1r^{n-1}\]
That's the formula for a geometric sequence.
a1 = 30, the number on the first day.
r = 2 because that's what we're multiplying by
Plug them in to get the general formula

Answer 16

Part 3: Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario. This is the one where they ask for the formula and to create a scenario to solve

Answer 17

The scenario will be something like how many minutes total did he spend at the gym for the first ___ days. Then you can pick the number of days and use the geometric sum formula. Pick a number while I look that one up

Answer 18

The sum of the first n terms of a geometric series is
\[S_n=a_1\frac{ 1-r^n }{ 1-r }\]

Answer 19

a_1 = 30, r = 2 from above. And n = the number of days

Answer 20

Ok I will start solving to see what I get

Answer 21

Ok I got s=210/n I choose 3 for the number of days

Answer 22

yes, that's right.

Answer 23

Thanks you so much for helping I'm taking an Alegebra class online and there's this project which were the questions I asked because I submitted it the first time and I got a 70% and the second a 30% so this is my last time right now I have a low C in the class and the project counts as 3 test grades which could help boost up my grade a lot plus I need to pass the class with a A or B to get into the high school I want to go to I really suck at math

Answer 24

Could you help me with 2 more questions if you can

Answer 25

Well good luck. You seem like you've got a solid understanding :).

Answer 26

I've got to log off for a while, but post them. I'll be on later and I'll look for them. I'll give it a go if no one else answers.

Answer 27

Ok thank you

Answer 28

you're welcome.