Question

FAN AND MEDAL!!!!!!!!!!!!!!!!!!!!

You are having a discussion about sequences with your classmates. She insists that she the sequence 2, 3, 5, 8, 12 must be either arithmetic or geometric. IS she correct of incorrect? Explain.

Answer 1

@mathmale

Answer 2

an arithmetic sequencs has terms which have a common difference

eg 2, 4 , 6, 8

- each term is formed by adding 2 to the previous term

another example would be 2,5,8,11 (common difference = 3)


a geometric sequence has a common ratio - each term is formed from previous by multiplying by this ratio
eg

2 , 4,8 ,16

common ratio is 2


so what do you think ?

Answer 3

is there a common difference for 2 3 5 8 12?

Answer 4

No, it have to answer the question

Answer 5

correct 3-2 = 1
5-3 = 2
8-5 = 3

the difference is increasing for each term so it is not arithmetic


now try dividing second term by the first term

and third term by the second to see if there is a common ratio

Answer 6

3 / 2 =
5 / 3 =
8 / 5 =

Answer 7

do these give the same result?

Answer 8

If not your answer is neither

Answer 9

So she is incorrect

Answer 10

I think she si corrent

Answer 11

no - try working out those divisions and see if they give the same result - I think you'll find they dont - so it cant be a geometric sequence either.

Answer 12

3/2 = 1.5
5/3 = 1.67