## anonymous one year ago please help medal will be awarded Which sequence is modeled by the graph below?

1. anonymous

2. SolomonZelman

Ok, the x-coordinate is the number of the term, and y-coordinate is the term. $$\large\color{black}{ \displaystyle ( }$$ Such that $$\large\color{black}{ \displaystyle {\rm a}_{~x}~=~y~~) }$$

3. SolomonZelman

So, you have 3 points: (2,1) (3,3) (4,9) what these points mean, is that $$\large\color{black}{ \displaystyle a_2=1 }$$ $$\large\color{black}{ \displaystyle a_3=3 }$$ $$\large\color{black}{ \displaystyle a_4=9 }$$

4. SolomonZelman

so, can you see the pattern here?

5. anonymous

that goes up by 3

6. SolomonZelman

you mean multiplying times 3 each time, right?

7. anonymous

yes

8. SolomonZelman

ok.

9. SolomonZelman

Did they give you the question as it is, without any options to it?

10. anonymous

the options are an=1/3(27)^n-1 an= 27(1/3)^n-1 an= 1/3(3)^n-1 an= 3(1/2)^n-1

11. anonymous

i feel like it is the third one because of the pattern u told me

12. SolomonZelman

yes, it is the third one. (not because of the pattern that i told you, but because of the pattern that you noticed)

13. SolomonZelman

the recursive formulas in every other option besides C have a wrong common ratio (not r=3)

14. SolomonZelman

Any questions?

15. anonymous

yes

16. SolomonZelman

17. anonymous

Jeff is designing the seating arrangement for a concert in his high school theater. To give everyone a good view, each row must have 5 more seats than the row before it, and the 1st row can only have 12 seats. Help Jeff plan the rest of the seating by solving for how many seats are in row 25. Then explain to Jeff how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences

18. anonymous

im really confused

19. SolomonZelman

So, lets do this piece by piece. each row has 5 more seats than the row before it $$\large\color{black}{ \displaystyle \left(a_{n+1}\right) =\left(a_1\right)+5 }$$ and the first row can only have 12 seats. $$\large\color{black}{ \displaystyle a_{1}=12 }$$ help Jeff plan the rest of the seating by solving for how many seats are in row 25 find $$\large\color{black}{ \displaystyle a_{25} }$$

20. SolomonZelman

I wrote a phrase in gray, and below, a conversion of the statement into math.... is this understandable?

21. anonymous

yes

22. anonymous

is a25 =300

23. anonymous

so that means its 480

24. SolomonZelman

lets, see... based on the first statement we know the common difference is 5. (that is d=5) $$\large\color{black}{ \displaystyle a_{n}=a_1+5(n-1) }$$ plugging in our information $$\large\color{black}{ \displaystyle a_{25}=12+5(25-1) }$$

25. SolomonZelman

$$\large\color{black}{ \displaystyle a_{25}=12+5(25-1) }$$ $$\large\color{black}{ \displaystyle a_{25}=12+5(24) }$$ $$\large\color{black}{ \displaystyle a_{25}=12+5(20) +5(4) }$$ $$\large\color{black}{ \displaystyle a_{25}=12+100 +20 }$$ $$\large\color{black}{ \displaystyle a_{25}=132 }$$

26. SolomonZelman

i am writing it out like this, because I don't have a calc near by...

27. anonymous

so how do you create an equation

28. SolomonZelman

create which equation"?

29. anonymous

to predict the number of seats in any row

30. anonymous

i guess the answer will be Row one= 12 Row two= 12 + 5 The equation will be: Row n = 12+5(n-1) Where n is random number, the row will have 12 seats plus 5 for every row higher than 1. So row 25 will have 12 + 5*(25-1) 12+24*5=12+120=132 Row 25 will have 132 seats.

31. SolomonZelman

yes

32. anonymous

33. SolomonZelman

ok... i will try my best

34. anonymous

Tommy has \$350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.04)^x − 1. After combining the two functions, his new function is g(x) = 350(1.04)^x − 1. Using complete sentences, explain what this new function means

35. SolomonZelman

okay.

36. anonymous

im really confused again