Question

10, 10.1, 10.01, 10.001, 10.0001,.... is this arithmetic sequence

Answer 1

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive numbers is the same. So, for example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence, because the difference between any two consecutive numbers is 3. The difference between 2 and 5 is 3, so is the difference between 8 and 11, 11 and 14, any two consecutive numbers in the sequence that you choose.

So, with that in mind, is the sequence in your question an arithmetic sequence?

Answer 2

so no because right away between the first numbers its .1 but between the second pair its -0.09

Answer 3

does it havve to follow the positive and negative sign? @nbouscal

Answer 4

Yes. For instance, 9, 6, 3, 0, -3, -6... keeps the same sign until it goes above or below 0. Geometric sequences however can change signs because the common ratio can be negative numbers.

Answer 5

Yes, the difference has to be the same, whether it's positive or negative. And you are correct, the sequence in this problem is not arithmetic.

Answer 6

so say like the sequence is 3, -3, 3 -3, 3 sooo its six and negative six does that mean its not arithmetic. @nbouscal

Answer 7

Correct. That sequence is actually geometric. Each term is multiplied by -1 to get the next term.