Question

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

Answer 1

Explanation:

if arithmetic, then there is a common difference

if geometric, then there is a common ratio

to find the common ratio or difference

if you subtract successive terms from each other, they should have the same result if it is aritmetic

if you divide successive terms by each other, they should have the same result if it is geometric

2,3 and 5

3-2=1

5-3=2

2≠1

not aritmetic

3/2=1.5

5/3=1.66666

1.5≠1.6666

not geometric

she is wrong

Answer 2

if arithmetic, then there is a common difference
if geometric, then there is a common ratio

to find the common ratio or difference

if you subtract successive terms from each other, they should have the same result if it is aritmetic
if you divide successive terms by each other, they should have the same result if it is geometric


2,3 and 5

3-2=1
5-3=2
2≠1
not aritmetic

3/2=1.5
5/3=1.66666
1.5≠1.6666
not geometric

she is wrong