Question

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, ...

Answer 1

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

Answer 2

ok

Answer 3

its d/

Answer 4

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.

Answer 5

because it goes up by -7

Answer 6

you mean E?

Answer 7

yea

Answer 8

/lol

Answer 9

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

Good job!

Answer 10

thx

Answer 11

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

Answer 12

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

Answer 13

wait

Answer 14

check all that apply

Answer 15

theres more

Answer 16

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...

Answer 17

can you name some?

Answer 18

c

Answer 19

Yes, (d=1)

Answer 20

so yes is right

Answer 21

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

Answer 22

8ummmmmm

Answer 23

a

Answer 24

Yes, A (d=17)

Answer 25

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

Answer 26

thx

Answer 27

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

Answer 28

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

Answer 29

Any questions about anything said in this post?

Answer 30

nosir

Answer 31

i got one more question

Answer 32

Sure:)

Answer 33

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

Answer 34

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

Answer 35

yes

Answer 36

\(a_1\) is the very first radius

Answer 37

\(a_2\) is the second radius

Answer 38

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

Answer 39

yep

Answer 40

So, lets take a look at the given information.

Answer 41

\(\color{black}{a_1=2.40}\)
\(\color{black}{a_2=2.43}\)
\(\color{black}{a_3=2.46}\)
\(\color{black}{a_4=2.49}\)
\(\color{black}{a_5=2.52}\)

Answer 42

What is the common difference here?

Answer 43

0.03

Answer 44

Yes, that is correct!

Answer 45

I assume you have seen the following formula previously:

\(\color{black}{\large a_n=a_1+{\rm d}\cdot (n-1)}\)

Answer 46

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).

Answer 47

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

\(\color{black}{\large a_{85}=?}\)

Answer 48

4.92

Answer 49

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

Answer 50

thx

Answer 51

yw