Question

Please not only tell me but show me: Determine whether each sequence is arithmetic,geometric, or neither and find the tenth term.

a.) 23,27,31,35,39...
b.)-12,-5,2,9,16,...
c.)-5,-15,-45,135,-405...

Answer 1

in an arithmetic sequence you add the same number every time. If you look a you see that it goes up by 4 each time, making it arithmetic.

Looking at b you see that it increases by 7 each time, making it arithmetic.

at c it looks almost geometric, but at 135 it breaks the pattern, so it is neither

Answer 2

Arithmetic depends on whether the sequence has a common difference from term to term, through adding or subtracting. Sequence A has 4 being added to each term.
Geometric has each previous term being put into an equation. Like 4x-(5x * 4) or something. And each term comes out in compliance to that equation. I Don't remember how to get the formula but it has to do with the terms. perhaps @johnweldon1993 can assist you. if a sequence doesn't follow either of the rules, it will be neither. Also, to get the 10th term you can simply follow the patter, or use the sigma notation.

Answer 3

Okay, I understand the difference between the patterns, but when you look at the pattern of C, that's where I'm really confused lol. Can you help me with that?

Answer 4

Well C...As you can see..the pattern looks to start off at the numbers being multiplied by 3....but what happens after that? It goes to positive.....it cant be geometric now...and we know it isn't arithmetic... so it is neither.

Answer 5

That's because there is no pattern in C.
It looks like you keep multiplying 3 every time, but see how the fourth term is 135 instead of -135 as you would expect.
It's not a geometric sequence, and neither is it arithmetic.

Answer 6

But how do I get to the tenth term?

Answer 7

When you add or subtract to get each next term - the sequence is arithmetic
When you multiply or divide to get each next term - the sequence is arithmetic
if there is no pattern that works for all "from-term-to-next-term" - the sequence is not arithmetic or geometric. (i.e. it is NOT a SEQUENCE)

Answer 8

So trick question, there is no way to get the tenth term, right?

Answer 9

yeah, the third was pretty much a trick question.
also, it is still a sequence, Zelman, just not an arithmetic or geometric one ^_^

Answer 10

:) oops

Answer 11

as long as c) does not have a typo... if it says -135, then it is geometric (multiply by 3 to get the next term)