The following sequence of numbers is an arithmetic sequence.
10, 10.1, 10.01, 10.001, 10.0001, ...
A. True
B. False

- anonymous

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- schrodinger

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- tkhunny

1) Don't post problems with no work shown.
2) An arithmetic sequence is characterized by what?

- anonymous

A

- anonymous

you dont have to be a jerk @tkhunny

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- anonymous

im sorry im not on a computer that i can show workon

- anonymous

Gee thnx...........

- tkhunny

No one is being a jerk. I have suggested the actual rules you agreed to follow when you created a User ID. Show your work. There is no excuse for any other behavior.
Please ignore the answer supplied by Sydney and answer my question. The answer will lead you to a correct solution.

- tkhunny

Hogwash. If you can type words, you can communicate your work. Answer my question.

- tkhunny

@sydneymmelin You're welcome to hang around and see the correct solution if you like.
Who will answer the question? What characterizes an Arithmetic Sequence?

- mathmale

It may help if you find and type in an example of an arithmetic sequence and then do the same for an example of a geometric sequence. Knowledge of the formats of these two different types of sequences is essential if you're to correctly answer the problem at hand.

- tkhunny

?? Isn't that the same question I asked? Who will answer it?

- anonymous

the same change over and over to the numbers.

- tkhunny

Excellent. Do that to two pairs of numbers
10.1 - 10.0 = ??
10.01 - 10.1 = ??
Do you get the same thing?

- mathmale

Dawson: I can see some truth and some fact in your response. Just with it were clearer. What kind of "change" are you talking about?
And, Dawson, I'd like for you to provide an example of a geometric sequence.

- anonymous

no

- anonymous

decimal change?

- tkhunny

Done. Not Arithmetic and move on to the next problem. Good work.
For Geometric Sequences, do the same thing, only use division, rather than subtraction.

- anonymous

or the placement of the one

- mathmale

Show us what you mean.

- mathmale

Dawson, show us what you mean by "change over and over to the numbers." when discussing "arithmetic sequence". Why not save time by looking up the formulas for arith. and geom. sequences?

- mathmale

With those in front of you, answering this question should become easy.

- tkhunny

"same change"

- anonymous

|dw:1450120116434:dw|

- mathmale

So, if we're given the first and second terms of a sequence (type unknown), as y ou have been given, what exactly is the "change" from the first to the second element of the sequence, for
1) an arith sequence ?
2) a geometric sequence ?

- tkhunny

Yes, the problem is designed so that you might become confused if you do not focus on the definition. Don't worry about the problem's attempts at distraction.
Arithmetic: Same Different between ANY successive pairs. 1, 2, 3, 4, 5
Geometric: Same Ratio between ANY successive pairs. 1, 2, 4, 8, 16
Neither: Anything else - as in this case. 1 1.1 1.01 1.001

- SolomonZelman

A0.B, A0.0B, A0.00B, A0.000B, A0.0000B,
(A and B are digits)
Would be,
\(\large\color{#000000 }{ \displaystyle \left\{A0+B\times10^{-n} {\color{white}{\LARGE |}}\right\}^{\infty}_{n=1} }\)
Is it possible to construct a pattern with A0 as the initial term?

- SolomonZelman

(tnx for opening the question because I have something to think about:) )

- mathmale

|dw:1450120481473:dw|

- anonymous

yes

- mathmale

which is it?

- mathmale

arith or geom?

- anonymous

geom

- SolomonZelman

\(a_{n+1}/a_{n}\)
Would not yield the same output (r - ratio) \(\forall\)n.
\(a_{n+1}-a_{n}\)
Would not yield the same output (d - difference) \(\forall\)n.

- SolomonZelman

(So, would your sequence satisfy the reuierements of arithmetic and/or geometric sequence?)

- anonymous

it would false right

- SolomonZelman

yes, I would say...
it is not an arithmetic sequence.

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