# Thread: Identify Sequence as Arithmetic, Geometric or Neither

1. ## Identify Sequence as Arithmetic, Geometric or Neither

I have to get all of them correct and for some reason I can't seem to get the right combination. How do you evaluate these?

For each the following sequences, enter "A" (without the quotation marks) if is arithmetic, "G" if it is geometric, and "N" if it is neither arithmetic, nor geometric.

Thank you!

2. Arithmetic Sequences are of the form $\displaystyle a+kd$
Hence, the difference of 2 consecutive terms gives a constant
Eg. 2,5,8,11

Geometric sequences are of the form $\displaystyle ar^k$
Hence, the quotient of 2 consecutive terms gives a constant
Eg. 2,6,18,54

No.1
$\displaystyle 1,\frac{1}{2},\frac{1}{3},\frac{1}{4}$
The difference of 2 consecutive terms is not constant
$\displaystyle 1-\frac{1}{2}=\frac{1}{2}, \frac{1}{2}-\frac{1}{3}=\frac{1}{6}$
The quotient of 2 consecutive terms is not constant
$\displaystyle \frac{\frac{1}{2}}{\frac{1}{3}}=\frac{3}{2}$

$\displaystyle \frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}$
Hence it is neither.

No.2
The difference of 2 consecutive terms gives a constant
Hence it is an arithmetic series.
The difference is $\displaystyle \frac{1}{2}$

You should try the rest on your own