## anonymous one year ago 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.

1. anonymous

@peachpi

2. anonymous

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.

3. anonymous

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

4. anonymous

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

5. anonymous

Wait did that even make sense what I just said

6. anonymous

He increases his time by half an hour

7. anonymous

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

8. anonymous

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

9. anonymous

does that make sense to you?

10. anonymous

So your basically multiplying by 20

11. anonymous

multiplying by 2

12. anonymous

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

13. anonymous

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?

14. anonymous

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

15. anonymous

$a_n=a_1r^{n-1}$ 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

16. anonymous

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

17. anonymous

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

18. anonymous

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

19. anonymous

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

20. anonymous

Ok I will start solving to see what I get

21. anonymous

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

22. anonymous

yes, that's right.

23. anonymous

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

24. anonymous

Could you help me with 2 more questions if you can

25. anonymous

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

26. anonymous

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.

27. anonymous

Ok thank you

28. anonymous

you're welcome.

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