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, ...

- anonymous

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- 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

ok

- anonymous

its d/

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- 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

because it goes up by -7

- SolomonZelman

you mean E?

- anonymous

yea

- anonymous

/lol

- SolomonZelman

yes, and the common difference is -7 (you add -7, as you said - which is completely correct).
Good job!

- anonymous

thx

- SolomonZelman

An alternating sequence is by definition not arithmetic, and thus must be excluded.

- SolomonZelman

Hold on, there might be other options.....

- anonymous

wait

- anonymous

check all that apply

- anonymous

theres more

- 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

can you name some?

- anonymous

c

- SolomonZelman

Yes, (d=1)

- anonymous

so yes is right

- SolomonZelman

there is a third correct answer
(so far E and C are correct)

- anonymous

8ummmmmm

- anonymous

a

- SolomonZelman

Yes, A (d=17)

- SolomonZelman

So, A, C & E are sequences that are arithmetic:)

- anonymous

thx

- 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

the difference is NOT ALWAYS the same, so for this reason B is NOT arithmetic....

- SolomonZelman

Any questions about anything said in this post?

- anonymous

nosir

- anonymous

i got one more question

- SolomonZelman

Sure:)

- 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

The distance of the loop of paper away from the center is the radius, right?

- anonymous

yes

- SolomonZelman

\(a_1\) is the very first radius

- SolomonZelman

\(a_2\) is the second radius

- SolomonZelman

and you need \(a_{85}\) - the 85th radius.

- anonymous

yep

- SolomonZelman

So, lets take a look at the given information.

- 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

What is the common difference here?

- anonymous

0.03

- SolomonZelman

Yes, that is correct!

- SolomonZelman

I assume you have seen the following formula previously:
\(\color{black}{\large a_n=a_1+{\rm d}\cdot (n-1)}\)

- 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

\(\color{black}{\large a_{85}=2.40+{\rm 0.03}\cdot (85-1)}\)
\(\color{black}{\large a_{85}=?}\)

- anonymous

4.92

- SolomonZelman

yes, that is right.
And that means that your 85th radius is 4.92 centimeters.

- anonymous

thx

- SolomonZelman

yw

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