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anonymous
 one year ago
WILL MEDAL
Can anyone comment the labeled functions for Arithmetic Series, Arithmetic Sequences, Geometric Series, and Geometric Sequences.?
anonymous
 one year ago
WILL MEDAL Can anyone comment the labeled functions for Arithmetic Series, Arithmetic Sequences, Geometric Series, and Geometric Sequences.?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Like the functions that solve them with a label that shows where everything should go. Say if the question was "Identify the 34th term of the arithmetic sequence 2, 7, 12 .."

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need serious help on this Topic

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[a_n=a_1+d(n1) \text{ is an arithemetic sequence with first term } a_1 \\ \text{ and common difference } d \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just replace d with 72 or 127 and then replace a_1 with 2 since it is the first term then enter in 34 for n use order of operations to find a_(34)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would be \[2_{34}=2_{1}+72(341)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1where did you get 2_(34)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you said replace n with 34

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes but what happen to the a_34?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and why didn't you replace a_1 with 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you replaced it with 2_1 whatever that means

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[a_n=a_1+d(n1) \\ a_1 \text{ is the first term } \\ d \text{ is the common difference } \\ a_1 \text{ was given as } 2 \\ \text{ you wanted to know } a_{34} \text{ this is why I said to replace } n \text{ with } 34\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.172 or 127 either of these differences will give you the common difference because this an arithmetic sequence 72=5 127=5 so d=5

freckles
 one year ago
Best ResponseYou've already chosen the best response.1anyways just follow order of operations to find a_(34)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What about arithmetic Series.?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1here is a sequence of numbers: \[a_1,a_2,a_3,a_4,...,a_n,...\] This is an arithmetic sequence if you have:\[a_1,a_1+d,a_1+2d,a_1+3d,a_1+4d,...,a_1+(n1)d,... \\ \text{ hope you are seeing that I'm using } \\ a_1=a_1 \\ a_2=a_1+d \\ a_3=a_1+2d \\ a_4=a_1+3d \\ ... \\ a_n=a_1+(n1)d \text{ or can be written as } a_n=a_1+d(n1) \\ \] An arithmetic series is just the summing of the terms of an arithmetic sequence. \[a_1,a_2,a_3,a_4,...,a_n,...\] This is a geometric sequence if you have: \[a_1,a_1 r,a_1r^2,a_1r^3,a_1r^4,...,a_1r^{n1},... \\ \text{ I hope you are seeing that I'm using } \\ a_1=a_1 \\ a_2=a_1r \\ a_3=a_1r^2 \\ a_4=a_1r^3 \\ a_5=a_1r^4 \\ ... \\ a_n=a_1r^{n1} \] A geometric series is just a summing of the terms of a geometric sequence.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Are you wanting the sum formulas ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im still trying to fully comprehend this. I'm not very good at math :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the difference between a series and a sequence.? (Just to add to my notes)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you know what sum means?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1A series is a sum of the terms of a sequence.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I was just asking if you knew what sum meant because I basically already said this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sum is the outcome of adding 2 or more number together.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\text{ Sequence of numbers looks like } a_1,a_2,a_3,...,a_n,... \\ \text{ a Series looks like } a_1+a_2+a_3+...+a_n+...\] notice a series is just as I said the sum of the terms of a sequence

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you might also have seen this notation for the series: \[\sum_{i=1}^{n}a_i\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Also a series doesn't always have to start at i=1 and end at n

freckles
 one year ago
Best ResponseYou've already chosen the best response.1A series can be infinite. And it can also start at i=2 etc...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for all your help man, i really appreciate it.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if you want to know the sum formula for an arithmetic series: \[\sum_{i=1}^{n}(a_1+d(i1)) \\ \sum_{i=1}^{n}a_1 + \sum_{i=1}^{n}di\sum_{i=1}^{n}d \\ a_1n+d \frac{n(n+1)}{2}dn \\ \frac{2a_1n}{2}+\frac{dn(n+1)}{2}\frac{2dn}{2} \\ \frac{2a_1n+dn^2+dn2dn}{2} \\ \frac{n(2a_1+dn+d2d)}{2} \\ \frac{n}{2}(2a_1+dnd) \\ \frac{n}{2}(a_1+a_1+d(n1)) \\ \frac{n}{2}(a_1+a_n) \\ \frac{n(a_1+a_n)}{2} \\ \text{ so \in conclusion } \\ \sum_{i=1}^{n}(a_i+d(n1))=\frac{n(a_1+a_n)}{2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1all this is saying if you aren't used to sigma notation is that: \[(a_1)+(a_1+d)+(a_1+2d)+\cdots +(a_1+(n1)d)=\frac{n(a_1+a_n)}{2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\sum_{i=1}^{n}a_1 r^{i1}=a_1 \sum_{i=1}^{n} r^{i1}=a_1 \frac{r^n1}{r1}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and that is the sum formula for a geometric series

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and again if you aren't used to sigma notation that just says: \[(a_1)+(ra_1)+(r^2a_1)+\cdots +(r^na_1)=a_1\frac{r^n1}{r1}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if the geometric series is infinite though then you have.. \[\sum_{i=1}^{\infty}a_1r^{i1}=a_1 \frac{1}{1r} \text{ which only converges for } r<1\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1anyways post a few new questions and try to actually practice with these formulas this will still be meaningless to you without some practice
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