# Identify Sequence as Arithmetic, Geometric or Neither

• Dec 3rd 2009, 12:21 PM
thebristolsound
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.

http://webwork1.math.utah.edu/webwor...c843dbca81.png

http://webwork1.math.utah.edu/webwor...097122a031.png

http://webwork1.math.utah.edu/webwor...bb89717401.png

http://webwork1.math.utah.edu/webwor...1fe301e911.png

http://webwork1.math.utah.edu/webwor...f83eab8771.png

http://webwork1.math.utah.edu/webwor...3d3f048c31.png

Thank you!
• Dec 3rd 2009, 12:35 PM
I-Think
Arithmetic Sequences are of the form $a+kd$
Hence, the difference of 2 consecutive terms gives a constant
Eg. 2,5,8,11

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

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

The quotient of 2 consecutive terms is not constant
$\frac{\frac{1}{2}}{\frac{1}{3}}=\frac{3}{2}$

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

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

You should try the rest on your own