Year 12s: what will be the first way you research your future options? >>

Why is y,y^1,y^2,y^3..not an arithmetic sequence??

Why is y,y^1,y^2,y^3..not an arithmetic sequence, I thought this sequence meant there are common difference between them, and in this case, it multiplies by y each time?
SOMEONE HELP PLZ

Reply 1

zeldor711

Original post by Sizzo1128

Why is y,y^1,y^2,y^3..not an arithmetic sequence, I thought this sequence meant there are common difference between them, and in this case, it multiplies by y each time?
SOMEONE HELP PLZ

An arithmetic sequence has a common difference, and a geometric sequence has a common multiple (in this case y).

Reply 2

Pangol

Original post by Sizzo1128

Why is y,y^1,y^2,y^3..not an arithmetic sequence, I thought this sequence meant there are common difference between them, and in this case, it multiplies by y each time?
SOMEONE HELP PLZ

What you are describing is a different kind of sequence, called a geometric sequence. As you say, with an arithmetic sequence, there is a common difference each time - that is, the difference between any two successive terms is always the same. Let's look at an example of the kind of sequence you are talking about with y = 2. That sequence would be 2, 4, 8, 16, 32, ... The differences between successive terms are 2, 4, 8, 16, ... . As you can see, these are not all the same.

What level are you looking at this from? A level includes the study of arithmetic and geometric sequences, and as you can see, there are some differences between the way that they have to be handled.

Reply 3

thekidwhogames

Arithmetic sequence is one that has a common difference between each term - e.g. 1, 2, 3, 4, etc. (this is also the set of natural numbers). Another arithmetic sequence can be y, 2y, 3y, 4y, etc.

A geometric sequence is one with a common ratio (or common multiple); e.g. 2, 4, 8, 16 (multiplies by 2 each time). What you are referring to is a geometric sequence with common ratio y - it gets multiplied by y each term.

Reply 4

Chichaldo

Original post by Sizzo1128

Why is y,y^1,y^2,y^3..not an arithmetic sequence, I thought this sequence meant there are common difference between them, and in this case, it multiplies by y each time?
SOMEONE HELP PLZ

An example of your sequence is 2, 2, 4
First difference is 0
Second difference is 2
As they are not the same difference each time, it is not an arithmetic sequence.

Reply 5

Sizzo1128

Original post by zeldor711

An arithmetic sequence has a common difference, and a geometric sequence has a common multiple (in this case y).

Ohhhhh,so it is a geometric sequence. THANK YOU SO MUCH

Reply 6

Sizzo1128

Original post by thekidwhogames

Thank you for your clear explanation. I finally get it!!

Reply 7

Sizzo1128

Original post by Chichaldo

An example of your sequence is 2, 2, 4
First difference is 0
Second difference is 2
As they are not the same difference each time, it is not an arithmetic sequence.

Thank you for solving my problem and making it clear!!!!!!! Now I know where I went wrong

Reply 8

sindyscape62

Original post by Sizzo1128

Ohhhhh,so it is a geometric sequence. THANK YOU SO MUCH

No, what you've got in NOT a geometric sequence either.

The first two terms of it are the same, so to get from the first to second term you multiply by 1, but to get from the second to the third you multiply by y. For the geometric sequence what you multiply by has to be the same each time.

For it to be a geometric sequence the first term could to be 1, not y. You could also just remove the first term, which would also make it a geometric sequence.