anonymous
  • anonymous
Help with arithmetic/geometric sequences and series problem please
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
The problem is in the attached file
anonymous
  • anonymous
what does is mean by describe the four quantities? Don't the quantitates mean the same thing in all four formulas?
freckles
  • freckles
the quantities are the the variables like a_1,n,d,a_n in the problem a and a_1,n,r,a_n in problem c

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freckles
  • freckles
do you know what a_1 means?
freckles
  • freckles
the subscript there basically tells you
freckles
  • freckles
for example a_6 is the 6th term in the sequence
freckles
  • freckles
which choice a or c represents an arithmetic sequence ? and of those choices one if a geometric sequence. an example of an arithmetic sequence is 3,7,11,15,... notice each term minus it's previous is the same number this number is the common difference an example of a geometric sequence is 2,4,8,16,... notice each term divided by its previous is the same number this number is the common ratio what do you think the d represents ? what do you think the r represents?
anonymous
  • anonymous
d represents the difference and r represents the common ratio @freckles
freckles
  • freckles
great d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence
anonymous
  • anonymous
I'm confused though because in the problem it says to describe the four quantities for each formula, but would the quantities be the same in each formula
anonymous
  • anonymous
for example wouldn't a_1 mean the first term in the sequence no matter what formula it is?
anonymous
  • anonymous
@freckles
freckles
  • freckles
yes a_1 can mean the first term in the sequence
anonymous
  • anonymous
ok, so how do I answer the second part of the question? @freckles
freckles
  • freckles
I don't know which 3 to use for example in a do they want us to use a_1, n, and d to find a_n or do they want us to use a_1,a_n,n to find d or do they want us to use a_n,n,d to find a_1 or do they want us to use a_1,a_n,d to find n or do they want us to do each possibility of what they could mean
anonymous
  • anonymous
I'm not sure about that either, I'm assuming they want us todo each possibility. Could you just show me how to do it for 1 of the formulas and I can figure it out for the other ones? @freckles
freckles
  • freckles
\[a_n=a_1+d(n-1) \\ \text{ if we have } a_1,d, \text{ and } n \text{ just follow the order of operations \to find } a_n \\ \\ a_n=a_1+d(n-1) \\ \\ \text{ if we have } a_n,a_1,n \text{ then we can find } d \text{ by doing } \\ a_n-a_1=d(n-1) \text{ subtract } a_1 \text{ on both sides } \\ \frac{a_n-a_1}{n-1}=d \text{ divided both sides by} (n-1) \\ \] then you can do something similar for the other two possibilties just solve the equation for n also solve the equation for a_1
anonymous
  • anonymous
ok so it's pretty simple
anonymous
  • anonymous
thanks!

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