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, ...

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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
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a sequence that follows a pattern where you add the same number each time, or subtract the same number each time - is arithmetic sequence.
ok
its d/

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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.
because it goes up by -7
you mean E?
yea
/lol
yes, and the common difference is -7 (you add -7, as you said - which is completely correct). Good job!
thx
An alternating sequence is by definition not arithmetic, and thus must be excluded.
Hold on, there might be other options.....
wait
check all that apply
theres more
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...
can you name some?
c
Yes, (d=1)
so yes is right
there is a third correct answer (so far E and C are correct)
8ummmmmm
a
Yes, A (d=17)
So, A, C & E are sequences that are arithmetic:)
thx
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
the difference is NOT ALWAYS the same, so for this reason B is NOT arithmetic....
Any questions about anything said in this post?
nosir
i got one more question
Sure:)
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
The distance of the loop of paper away from the center is the radius, right?
yes
\(a_1\) is the very first radius
\(a_2\) is the second radius
and you need \(a_{85}\) - the 85th radius.
yep
So, lets take a look at the given information.
\(\color{black}{a_1=2.40}\) \(\color{black}{a_2=2.43}\) \(\color{black}{a_3=2.46}\) \(\color{black}{a_4=2.49}\) \(\color{black}{a_5=2.52}\)
What is the common difference here?
0.03
Yes, that is correct!
I assume you have seen the following formula previously: \(\color{black}{\large a_n=a_1+{\rm d}\cdot (n-1)}\)
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).
\(\color{black}{\large a_{85}=2.40+{\rm 0.03}\cdot (85-1)}\) \(\color{black}{\large a_{85}=?}\)
4.92
yes, that is right. And that means that your 85th radius is 4.92 centimeters.
thx
yw

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