anonymous
  • anonymous
Which of the following sequences of numbers are arithmetic sequences? Check all that apply. A. 54, 71, 88, 105, 122, ... B. 154, 71, 8, 5, 2, ... C. 345, 346, 347, 348, 349, ... D. 12, -24, 36, -48, 56, ... E. -3, -10, -17, -24, -31, ...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
a sequence that follows a pattern where you add the same number each time, or subtract the same number each time - is arithmetic sequence.
anonymous
  • anonymous
ok
anonymous
  • anonymous
its d/

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More answers

SolomonZelman
  • SolomonZelman
For example: `1, 4, 7, 10, 13 ....` here you are adding 3 every time, and this is why it is an arithmetic sequience. ---------------------------------------------------- example #2: `6, - 10, -26, -52,....` here you are subtracting 16 every time, and this is why it is an arithmetic sequience.
anonymous
  • anonymous
because it goes up by -7
SolomonZelman
  • SolomonZelman
you mean E?
anonymous
  • anonymous
yea
anonymous
  • anonymous
/lol
SolomonZelman
  • SolomonZelman
yes, and the common difference is -7 (you add -7, as you said - which is completely correct). Good job!
anonymous
  • anonymous
thx
SolomonZelman
  • SolomonZelman
An alternating sequence is by definition not arithmetic, and thus must be excluded.
SolomonZelman
  • SolomonZelman
Hold on, there might be other options.....
anonymous
  • anonymous
wait
anonymous
  • anonymous
check all that apply
anonymous
  • anonymous
theres more
SolomonZelman
  • SolomonZelman
Lets go in order. We know E is arithmetic (d=-7) We know D is NOT arithmetic (because the sign alternates) yes, thre is more...
SolomonZelman
  • SolomonZelman
can you name some?
anonymous
  • anonymous
c
SolomonZelman
  • SolomonZelman
Yes, (d=1)
anonymous
  • anonymous
so yes is right
SolomonZelman
  • SolomonZelman
there is a third correct answer (so far E and C are correct)
anonymous
  • anonymous
8ummmmmm
anonymous
  • anonymous
a
SolomonZelman
  • SolomonZelman
Yes, A (d=17)
SolomonZelman
  • SolomonZelman
So, A, C & E are sequences that are arithmetic:)
anonymous
  • anonymous
thx
SolomonZelman
  • SolomonZelman
D is NOT arithmetic, because the sign alternates. ------------------------------------------- B is obviously NOT arithmetic, because there is no [same] common difference. 154 - 71 \(\ne\) 71 - 8 \(\ne\) 8 - 5
SolomonZelman
  • SolomonZelman
the difference is NOT ALWAYS the same, so for this reason B is NOT arithmetic....
SolomonZelman
  • SolomonZelman
Any questions about anything said in this post?
anonymous
  • anonymous
nosir
anonymous
  • anonymous
i got one more question
SolomonZelman
  • SolomonZelman
Sure:)
anonymous
  • anonymous
A roll of paper towels is wound around a hollow cardboard tube. The cardboard tube in the middle of the roll has an outside radius of 2.4 cm. The thickness of the paper is 0.3 mm. The sequence of distances of the loops of paper away from the center of the roll (in centimeters) is the following: a1, a2, a3, a4, a5, & = 2.40, 2.43, 2.46, 2.49, 2.52, & What is the radius of the 85th loop of paper, starting from the center of the tube? A. 4.89 cm B. 4.92 cm C. 4.86 cm D. 4.95 cm
SolomonZelman
  • SolomonZelman
The distance of the loop of paper away from the center is the radius, right?
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
\(a_1\) is the very first radius
SolomonZelman
  • SolomonZelman
\(a_2\) is the second radius
SolomonZelman
  • SolomonZelman
and you need \(a_{85}\) - the 85th radius.
anonymous
  • anonymous
yep
SolomonZelman
  • SolomonZelman
So, lets take a look at the given information.
SolomonZelman
  • SolomonZelman
\(\color{black}{a_1=2.40}\) \(\color{black}{a_2=2.43}\) \(\color{black}{a_3=2.46}\) \(\color{black}{a_4=2.49}\) \(\color{black}{a_5=2.52}\)
SolomonZelman
  • SolomonZelman
What is the common difference here?
anonymous
  • anonymous
0.03
SolomonZelman
  • SolomonZelman
Yes, that is correct!
SolomonZelman
  • SolomonZelman
I assume you have seen the following formula previously: \(\color{black}{\large a_n=a_1+{\rm d}\cdot (n-1)}\)
SolomonZelman
  • SolomonZelman
1) you have to find the 85th term, so you would plug in n=85. 2) you know the first term is 2.40 (so you plug in \(a_1=2.40\) 3) you know the common difference is 0.03 (so plug in d=0.03).
SolomonZelman
  • SolomonZelman
\(\color{black}{\large a_{85}=2.40+{\rm 0.03}\cdot (85-1)}\) \(\color{black}{\large a_{85}=?}\)
anonymous
  • anonymous
4.92
SolomonZelman
  • SolomonZelman
yes, that is right. And that means that your 85th radius is 4.92 centimeters.
anonymous
  • anonymous
thx
SolomonZelman
  • SolomonZelman
yw

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