I need help............ I don't know how to convert f(n)=f(n-1)+d into the sequence notation a(subscript) n=a+d(n-1)

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I need help............ I don't know how to convert f(n)=f(n-1)+d into the sequence notation a(subscript) n=a+d(n-1)

Mathematics
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is that all it says? or is there more that's given?
No it says "Use your scenario to write the function for the 7th term in your sequence using sequence notation".

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this is what i filled in Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for 20 minutes on Monday. Every day she increases her practice time by 4 . 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.
20 mins , increases , time by 4 that's what i added
so they want you to make up a sequence of your own? or can we use this example?
they wanted me to make up my own based upon what i filled in and the formula above with the a
ok what sequence did you make up on your own?
a(subscript) n=a+d(n-1)
that is what help on filling in on this equation. In the f(n) version it made up one which is f(7)=f(6-1)+4
when i fill in the sequence equation it looks like this a(subscript)7=a+4(7-1)
it says `Jasmine practices the piano for 20 minutes on Monday` so the first term of this sequence is 20 making a = 20
the next day, tuesday, would be a+d = 20+4 = 24 min ------------------------- wednesday would be 24+4 = 28 etc etc
so how would that be written
a = 20 and d = 4 they are plugged into `a+d(n-1)` to get the general nth term
so, a+d(n-1) = 20+4(n-1) = ???
thank you for you help.
glad to be of help
@jim_thompson5910 need you help again with another 1
go ahead
Use your scenario to write the formula for the 5th term in your sequence using sequence notation.
the equation for geometric sequence is an=a1•rn−1.
my info is Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.
`Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.` this is an ARITHMETIC sequence since the amount is increasing by a fixed amount. d = 5 is the amount going up each time
if you said maybe something like "increases by 5%", then it would work
i see what you're saying , I knew something wasn't right. So change it to 5%
then what would i do
the first term is a = 45 the common ratio is r = 0.05 (decimal form of 5%)
no sorry, the common ratio would be 1.05 1+0.05 = 1.05
so it would be a5=45 x1.05(7-1)
first term: 45 second term = (first term)*(common ratio) second term = (45)*(1.05) second term = 47.25 etc etc
change the 5% to 1.05%?
I added on 1 because increasing by 5% is the same as multiplying by 1.05
the nth term should be \[\Large a(r)^{n-1}\] then you plug in a = 45 and r = 1.05
ok
i have to use that exact equation above \[a _{4=45x 1.05(4}\]
the x= times
the exponent should be n-1 = 4-1 so \[\LARGE a_4 = 45*(1.05)^{4-1}\]
well no, because i want to find the 5th term. I simplified it so I didn't put the -1 i just did it.
so 5-1
oh, then you want to compute \(\LARGE a_5\) and not \(\LARGE a_4\)
yes it's a5 not a4
they wanted me to find a5 the fifth term.
I see
ok so the answer would be what i said rightttt
yes, it would be \[\LARGE a_5 = 45*(1.05)^{4}\]
Thank you, I may need help in like 3 mins again 1 more
ok
a_(5=45 ×〖1.05〗^(5-1) ) @jim_thompson5910
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.
I think you meant to write \[\LARGE a_5 = 45 \times 1.05^{5-1}\] right?
Yes, but i don't know how to make it look like that, how do you do that?
the geometric series formula Sn= a1−a1rn 1−r
you can use the equation editor (click the equation button below the text box) I typed in `\LARGE a_5 = 45 \times 1.05^{5-1}` surrounded by `\[` and `\]`
as for the summation formula, it would be \[\Large S_n = a*\frac{1-r^n}{1-r}\]
which is equivalent to the form you wrote
where the a is by itself it should be with the 1 at the top
yes the two are equivalent \[\Large S_n = a*\frac{1-r^n}{1-r} = \frac{a-a*r^n}{1-r}\]
I'm going to screenshot it
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yeah which is what I wrote here \[\Large S_n = \frac{a-a*r^n}{1-r}\]
there are 2 versions of the same thing really
ok
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they want you to add up a bunch of terms and use the Sn formula to do it quickly
so for instance, add up the first 8 terms and compute S8
So I"m using what you are saying as a example, because Idon't want to seem as a cheater
you can use another value of n
ok 5
Oh it says use the same scenario
from part 2
so a = 45 and r = 1.05
right ,but i need to make a question now
Maybe I can say Anthony goes to the gym at 10 am for 45mins, then IDK what im doing
so you have to make a completely different scenario?
no just use the scenario from part 2 to make up a question
i just seen an example on my math lesson so here is something similar "find the sum of the first 5 terms of the geometric series
but I don't know what numbers are suppose to be in the geometric series here is the example
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ok so you'll plug a = 45 and r = 1.05 into that Sn formula then you pick any n value you want (you picked n = 5 I think) and plug that in as well
\[\Large S_n = \frac{a-a*r^n}{1-r}\] \[\Large S_5 = \frac{45-45*1.05^5}{1-1.05}\] \[\Large S_5 = ???\]
is it like the example?
yes
ok than so what would be the geometric series than for the question?
I'm not sure what you're asking exactly?
because i need to write a question; in the example question in the lesson it has something in the question that says geometric series look at the screenshot again
I think it means 3 numbers that have a common ratio of 5%
you mean they want you to add up the first three terms of the geometric sequence?
idk honestly. I'm just listening to you
does it look like what it mean in the picture
this is a project and it doesn't really explain much
yeah I wish it had clearer instructions. I think they want you to add up a bunch of terms so say you wanted to add up the first 7 terms a = 45 r = 1.05 n = 7 \[\Large S_n = \frac{a-a*r^n}{1-r}\] \[\Large S_7 = \frac{45-45*1.05^7}{1-1.05}\] \[\Large S_7 = \frac{45-45*1.4071004}{1-1.05}\] \[\Large S_7 = \frac{45-63.319518}{1-1.05}\] \[\Large S_7 = \frac{-18.319518}{-0.05}\] \[\Large S_7 = 366.39036\] The approximate sum of the first 7 terms is 366.39036
So the question would be "Find the sum of the first 7 terms
yes the work shown above would apply to that question
Thank you, your name should say lifesaver. You just helped me finish out my math class.
I'm glad I could be of help

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