Question

Is 40,10,5/2,5/8 geometric or arithmetic

Answer 1

Answer:

Geometric because there is a common ratio of (1/4)

Step-by-step explanation:

To determine if a series is arithmetic there must be a common difference.  A common difference is when you take consecutive terms and find the difference (10 - 40 = -30).  Then to see if it holds true you apply it to the next term (10 - 30 = -20).  If they match, then there is a common difference.  In this case they do not match thus no common difference.

If it is geometric, then there is a common ratio.  A common ratio is when you divide the second term from the first (10/40 = 1/4).  Once you have the possible ratio you multiply the second term by the common ratio to see if it holds (10 * 1/4 = 5/2).  In this case it does hold, and thus a common ratio, and a geometric sequence.

Answer 2

Step-by-step explanation:

It is a geometric sequence because it has common ratio not common difference.

a = 40

$r = \frac{a2}{a1} = \frac{10}{40} = \frac{1}{4}$

$again \: \: \frac{a3}{a2} = \frac{ \frac{5}{2} }{10} = \frac{5}{20} = \frac{1}{4}$