anonymous
  • anonymous
Which of the numbers below could be terms in the sequence an = 3n + 16? A. 64 B. 48 C. 46 D. 61 please please help
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I believe the correct answer would be A,C,D, but PLEASe let me know :)
nincompoop
  • nincompoop
why not test your answer out math is not about guessing
anonymous
  • anonymous
@nincompoop I don't know how to test out the answer, which is why I'm stuck

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More answers

DebbieG
  • DebbieG
You can either: 1. set each answer = to the expression for the sequence and see if the solution is an integer; or 2. Start listing the sequence, see if those numbers come up when you get to a high enough n.
anonymous
  • anonymous
One way to do it is to rearrange the equation so it looks like this (assume the number you're testing is called b):\[b = 3n + 16\]\[b-16=3n\]\[\frac{b-16}{3} = n\] Basically, when you plug in a number for b, if it evaluates such that n is an *integer* then b is in the sequence.
anonymous
  • anonymous
@DebbieG if I want to approach this using your 2nd suggestion, how do I start listing the sequence if it is 3n+16? I'm confused about that part
anonymous
  • anonymous
For the 2nd suggestion, you would start with n=0 and plug it in. Then n=1, n=2, etc.
DebbieG
  • DebbieG
n=1: 3(1)+16=19 n=2: 3(2)+16=? n=3: 3(3)+16=? etc etc :)
anonymous
  • anonymous
@alexray19 thank you so much that really made it a lot easier! :) When I solved the equations with the formula you gave me I got 64=16, 46=10, and 61=15. I know B is out of the picture because it was .00000 something, but which ones would be correct? Does it have to be just 16 which would make the answer 64 or do 46 and 61 fall on the line as well?
anonymous
  • anonymous
@DebbieG thank you for clarifying! :)
DebbieG
  • DebbieG
I'm a little confused by your post... lol. I think you have the correct answers, but lets make sure you understand the reasoning. :) We are trying to see if a counting number n will give each of the results. If so, then that number IS a term in the sequence; if not, it isn't (because it falls between 2 terms in the sequence). A. 64=3n+16 48=3n n=16 which is an integer, so this is in the sequence, for n=16 B. 48 =3n+16 32=3n n=32/3 not an integer, so this is not in the sequence (notice that for n=10 we get a_n=46, and for n=11 we get a_n=49) C. 46 = 3n+16 30=3n n=10, so in the sequence D. 61=3n + 16 3n=45 n=15, so in the sequence That's really all there is to it - just solve for n, and see if it's a positive integer. :)
anonymous
  • anonymous
Ohhh wait, does it say \[an=3n+16\]exactly? Like is the letter "a" a variable too?
DebbieG
  • DebbieG
It's a sequence, so I'm interpreting that as \(\Large a_{n}\).
anonymous
  • anonymous
@DebbieG thank you! that makes sense, i just get confused when I have to put it into equation form, I didnt know how to do that at all.. thank you! @alexray19 its supposed to be a sub n :)
DebbieG
  • DebbieG
You're welcome. :)

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