Question

determine wether each sequence is arithmetic or geometric. if the sequence is arethmetic,give the common defference and if geometric,give the common ratio.

e.7,12,17,22,27
f.2,-6,18,-54,162
g.109,100,91,82,73
h.32,16,8,4,2

Answer 1

To be an Arithmetic sequence, you must get the same result if you have
"any number - its previous number is a constant"
that result is called the "common difference"
e.g. in e)
12-7 = 5
17-12 = 5
22-17 = 5 , looks like we have an arithmetic sequence with a difference of 5
etc

For a Geometric sequence , any number divided by its previous number must be the same quotient. That quotient is called the "common ratio"
e.g. h)
16/32 = 1/2
8/16 = 1/2
4/8 = 1/2
2/4 = 1/2
the same common ratio of 1/2 so it is a geometric sequence

You check the other two