OpenStudy (camerondoherty):

Pretty Easy Question i have most of it done

3 years ago
OpenStudy (camerondoherty):

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for 10 minutes on Monday. Every day she increases her practice time by 5 minutes. If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence. Use your scenario to write the function for the 7th term in your sequence using sequence notation. Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for 20 minutes on Monday. Every day he increases his gym time by 10%. 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. Use your scenario to write the formula for the 5th term in your sequence using sequence notation. 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 \[S_{n}\] in your scenario.

3 years ago
OpenStudy (camerondoherty):

i already created the scenarios i jus needa put the stuff in sequence notation and find the 7th term

3 years ago
OpenStudy (camerondoherty):

easier than it looks

3 years ago
OpenStudy (camerondoherty):

@dan815 help?

3 years ago
OpenStudy (camerondoherty):

whats sequence notation?

3 years ago
OpenStudy (dan815):

okay tell me your sceneario

3 years ago
OpenStudy (camerondoherty):

Thats the one it came with blanks and i filled them in

3 years ago
OpenStudy (camerondoherty):

i filled in the numbers

3 years ago
OpenStudy (dan815):

Sequence notation is like 1+2+3+4..... = \[\sum n \]

3 years ago
OpenStudy (camerondoherty):

o.o

3 years ago
OpenStudy (dan815):

oh okay then lets see what kinda arith seq we are dealing with

3 years ago
OpenStudy (camerondoherty):

i think its 80 minuites but i dont know how to present it

3 years ago
OpenStudy (dan815):

so we sharted with 10 2nd day = 10+5 3rd day = 10+5+5 4th day = 10 + 5+5+5 ... The sequence is going like 10+15+20+25.... Sn=10+5n, if u want n at 1st day being tuesday and 0th day being monday

3 years ago
OpenStudy (camerondoherty):

so Sn=x+n is the sequence notation?

3 years ago
OpenStudy (dan815):

The proper notation \[S_n=10+5(n-1)\] \[S_7=10+5(7-1)\\ S_7=10+30=40 \]

3 years ago
OpenStudy (camerondoherty):

me confused...

3 years ago
OpenStudy (camerondoherty):

what does the formula look like?

3 years ago
OpenStudy (dan815):

lik this \[S_n=10+5(n-1)\] You can also simplify this to be \[S_n=5+5n\]

3 years ago
OpenStudy (dan815):

where is the nth day we care about

3 years ago
OpenStudy (cp9454):

\[a _{n} = a + (n-1)d\] where d is your comman difference, and a is first term.

3 years ago
OpenStudy (dan815):

hmm how I explain this.. you know about lines or functions.. like x y 1 10 2 15 3 20 4 25 ... .... This is a linear equation as y is increasing by 5 everytime so a constant slope.. Find the slope and y intercept write this equation in y=mx+b form where x = the number of day we want and Y = practice time

3 years ago
OpenStudy (cp9454):

put n = 7 in above equation you will get your result.

3 years ago
OpenStudy (camerondoherty):

What is (n-1)?

3 years ago
OpenStudy (cp9454):

its the formula for general term of an A.P

3 years ago
OpenStudy (dan815):

hold on miracrown will teach you... she is a good explainer

3 years ago
OpenStudy (dan815):

@Miracrown

3 years ago
OpenStudy (camerondoherty):

lol

3 years ago
OpenStudy (cp9454):

let an A.P. be \[a _{1}, a _{2}, a _{3}, ...........................a _{n-1}, a _{n}\]

3 years ago
OpenStudy (camerondoherty):

im not getting what ur saying @cp9454

3 years ago
OpenStudy (camerondoherty):

@dan815 ur busy?

3 years ago
OpenStudy (cp9454):

\[a _{1}= a\] \[a _{2}= a+d\] \[a _{3}= a+2d\] . . . .\[a _{n} = a+(n-1)d\]

3 years ago
OpenStudy (cp9454):

here \[a_{n} is the nth term.\]

3 years ago
OpenStudy (camerondoherty):

???

3 years ago
OpenStudy (cp9454):

\[a _{n}\] is the nth term. you just need to put the values of first term, comman difference, and the term you want to find. for example you want to find the 7th term, your formula should be, \[a _{7}= a+(7-1)d\]

3 years ago
OpenStudy (camerondoherty):

what do the variables stand for?

3 years ago
OpenStudy (cp9454):

a is first term, d is comman difference, e.g. it is 5 in your case n is no. of terms.

3 years ago
OpenStudy (cp9454):

still not getting @camerondoherty

3 years ago
OpenStudy (cp9454):

listen, its a formula just use it and you will see, how it works. and you will easily be able to solve the problems. @camerondoherty

3 years ago
OpenStudy (camerondoherty):

i got it but what about the second one wouldnt the equation or formula be different?

3 years ago
OpenStudy (cp9454):

no its the univrsal formula it is apllicable to all the APs in the world.

3 years ago
OpenStudy (camerondoherty):

because its a geometric sequence

3 years ago
OpenStudy (dan815):

Yes okay for 2nd one you have a 10% increase so multiplied by 1.1 everytime

3 years ago
OpenStudy (camerondoherty):

oh ok

3 years ago
OpenStudy (camerondoherty):

so hold on let me make the equation for it

3 years ago
OpenStudy (cp9454):

GP has different formula

3 years ago
OpenStudy (camerondoherty):

\[S_{5}=20+1.1(5−1)\]

3 years ago
OpenStudy (dan815):

\[G_n=20*(1.1)^{n-1}\], for n>=1

3 years ago
OpenStudy (dan815):

close

3 years ago
OpenStudy (camerondoherty):

o

3 years ago
OpenStudy (camerondoherty):

So \[G _{5}=20\times(1.1)^1\]

3 years ago
OpenStudy (dan815):

we need multiplyig by 1.1 so day 1= 20 day 2 =20*1.1 day3= 20*1.1*1.1-=20*1.1^2 day4=20*1.1^3 day5=20*1.1^4 Dayn=20*1.1^(n-1)

3 years ago
OpenStudy (dan815):

to the power of 4

3 years ago
OpenStudy (camerondoherty):

oh whoops xD i was thinking of one but i knew it was 4

3 years ago
OpenStudy (dan815):

ok good :)

3 years ago
OpenStudy (camerondoherty):

Ill take that as a yes...

3 years ago
OpenStudy (dan815):

yes

3 years ago
OpenStudy (camerondoherty):

@dan815 ?

3 years ago
OpenStudy (camerondoherty):

and can someone explain to me how to do the last one?

3 years ago
OpenStudy (dan815):

Now its the sum of a geometric serives

3 years ago
OpenStudy (camerondoherty):

Sum of what geometic serives?

3 years ago
OpenStudy (dan815):

yeah so \[S_n=G_1 + G_2 + G_3...+G_n\] They want yo to find a formula for this now we know what G_n can be written as, lets say instead of 20, it was P, and instead of 1.1 it was r for rate \[S_n=P*r^1+P*r^2+...p*r^n\]

3 years ago
OpenStudy (dan815):

oops it should actually go lke this dont forget that n-1

3 years ago
OpenStudy (dan815):

\[S_n=P+P*r^1+P*r^2+...p*r^{n-1}\]

3 years ago
OpenStudy (camerondoherty):

say what? Im confused...

3 years ago
OpenStudy (dan815):

note the first term is P only since r^0 =1

3 years ago
OpenStudy (camerondoherty):

too many Ps' and Gs'

3 years ago
OpenStudy (camerondoherty):

xD

3 years ago
OpenStudy (camerondoherty):

Wait so they want me to write that?

3 years ago
OpenStudy (dan815):

okay wait, just a scenario for part 3 first, i dont think they want you to derive the formnula really... they maybe just expect you to know the formula

3 years ago
OpenStudy (dan815):

write a scenario*

3 years ago
OpenStudy (camerondoherty):

like the whole question thingy?

3 years ago
OpenStudy (camerondoherty):

if so: Mark goes to the park for ______ minutes on Sunday. Every day he _________his park time by ____________. If he continues this pattern, how many minutes will he spend at the park on the 5th day?

3 years ago
OpenStudy (dan815):

well ya it can be something simple tho like /how long has anthony worked out after 10 days in total

3 years ago
OpenStudy (dan815):

yeah expect the last question would be like how many mins will be spend at the park if you combine all 5 days

3 years ago
OpenStudy (camerondoherty):

Mark goes to the park for 40 minutes on Sunday. Every day he increases his park time by 20%. If he continues this pattern, how many minutes will he spend at the park on the 5th day?

3 years ago
OpenStudy (dan815):

will he*

3 years ago
OpenStudy (dan815):

Mark goes to the park for 40 minutes on Sunday. Every day he increases his park time by 20%. If he continues this pattern, how many minutes will he spent at the park on the first 5 days altogether?

3 years ago
OpenStudy (camerondoherty):

i said tht -_-

3 years ago
OpenStudy (dan815):

altogether! u dummy

3 years ago
OpenStudy (camerondoherty):

\[S _{5}=40(2.2)^{5-1}\]

3 years ago
OpenStudy (camerondoherty):

lol

3 years ago
OpenStudy (dan815):

no Cammy this one different its a sum of all the days from 1 to 5

3 years ago
OpenStudy (camerondoherty):

i dont get it...

3 years ago
OpenStudy (dan815):

we want ot know how much time he has spent at the part in total

3 years ago
OpenStudy (camerondoherty):

from day 1 to 5?

3 years ago
OpenStudy (dan815):

yes

3 years ago
OpenStudy (camerondoherty):

altogether? all added up?

3 years ago
OpenStudy (dan815):

yes, thats what that S means S is for a sum

3 years ago
OpenStudy (dan815):

Like what if I asked you to fine how much total time he spent at the park in like 7 days all combined... G_7 is only telling u his time for the 7th day not all the previous days together

3 years ago
OpenStudy (camerondoherty):

\(S _{5}=40(2.2)^{5-1}\) \(S _{4}=40(2.2)^{4-1}\) \(S _{3}=40(2.2)^{3-1}\) \(S _{2}=40(2.2)^{2-1}\) \(S _{1}=40(2.2)^{1-1}\)

3 years ago
OpenStudy (dan815):

noo lol that is G_1 , G_2 G_3.. G_5

3 years ago
OpenStudy (dan815):

S is the sum of it \[S_5=G_1+G_2+G_3+G_4+G_5\]

3 years ago
OpenStudy (camerondoherty):

lol whoops just change the S to G

3 years ago
OpenStudy (dan815):

okok soo now use that Sn formula if u have it already

3 years ago
OpenStudy (camerondoherty):

wait so theres another formula?!

3 years ago