Pretty Easy Question i have most of it done
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.
i already created the scenarios i jus needa put the stuff in sequence notation and find the 7th term
easier than it looks
@dan815 help?
whats sequence notation?
okay tell me your sceneario
Thats the one it came with blanks and i filled them in
i filled in the numbers
Sequence notation is like 1+2+3+4..... = \[\sum n \]
o.o
oh okay then lets see what kinda arith seq we are dealing with
i think its 80 minuites but i dont know how to present it
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
so Sn=x+n is the sequence notation?
The proper notation \[S_n=10+5(n-1)\] \[S_7=10+5(7-1)\\ S_7=10+30=40 \]
me confused...
what does the formula look like?
lik this \[S_n=10+5(n-1)\] You can also simplify this to be \[S_n=5+5n\]
where is the nth day we care about
\[a _{n} = a + (n-1)d\] where d is your comman difference, and a is first term.
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
put n = 7 in above equation you will get your result.
What is (n-1)?
its the formula for general term of an A.P
hold on miracrown will teach you... she is a good explainer
@Miracrown
lol
let an A.P. be \[a _{1}, a _{2}, a _{3}, ...........................a _{n-1}, a _{n}\]
im not getting what ur saying @cp9454
@dan815 ur busy?
\[a _{1}= a\] \[a _{2}= a+d\] \[a _{3}= a+2d\] . . . .\[a _{n} = a+(n-1)d\]
here \[a_{n} is the nth term.\]
???
\[a _{n}\] 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, \[a _{7}= a+(7-1)d\]
what do the variables stand for?
a is first term, d is comman difference, e.g. it is 5 in your case n is no. of terms.
still not getting @camerondoherty
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
i got it but what about the second one wouldnt the equation or formula be different?
no its the univrsal formula it is apllicable to all the APs in the world.
because its a geometric sequence
Yes okay for 2nd one you have a 10% increase so multiplied by 1.1 everytime
oh ok
so hold on let me make the equation for it
GP has different formula
\[S_{5}=20+1.1(5−1)\]
\[G_n=20*(1.1)^{n-1}\], for n>=1
close
o
So \[G _{5}=20\times(1.1)^1\]
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)
to the power of 4
oh whoops xD i was thinking of one but i knew it was 4
ok good :)
Ill take that as a yes...
yes
@dan815 ?
and can someone explain to me how to do the last one?
Now its the sum of a geometric serives
Sum of what geometic serives?
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 \[S_n=P*r^1+P*r^2+...p*r^n\]
oops it should actually go lke this dont forget that n-1
\[S_n=P+P*r^1+P*r^2+...p*r^{n-1}\]
say what? Im confused...
note the first term is P only since r^0 =1
too many Ps' and Gs'
xD
Wait so they want me to write that?
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
write a scenario*
like the whole question thingy?
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?
well ya it can be something simple tho like /how long has anthony worked out after 10 days in total
yeah expect the last question would be like how many mins will be spend at the park if you combine all 5 days
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?
will he*
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?
i said tht -_-
altogether! u dummy
\[S _{5}=40(2.2)^{5-1}\]
lol
no Cammy this one different its a sum of all the days from 1 to 5
i dont get it...
we want ot know how much time he has spent at the part in total
from day 1 to 5?
yes
altogether? all added up?
yes, thats what that S means S is for a sum
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
\(S _{5}=40(2.2)^{5-1}\) \(S _{4}=40(2.2)^{4-1}\) \(S _{3}=40(2.2)^{3-1}\) \(S _{2}=40(2.2)^{2-1}\) \(S _{1}=40(2.2)^{1-1}\)
noo lol that is G_1 , G_2 G_3.. G_5
S is the sum of it \[S_5=G_1+G_2+G_3+G_4+G_5\]
lol whoops just change the S to G
okok soo now use that Sn formula if u have it already
wait so theres another formula?!
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