Determine whether each sequence is arithmetic or geometric?

Question

1.) 1, 2/5, 4/25, 8/125 
2.) 6, 2, -2, -6 
3.) -25, -20, -15, -10 
4.) 6, -3, 3/2, -3/4

Answer 1

Geometric series :

A sequence made by multiplying by some value each time.

Common ratio r = the ratio between any two consecutive numbers.

Arithmetic series :

A sequence made by adding by some value each time.

Common difference d = difference between any two consecutive numbers.

 

1) 1, 2/5, 4/25, 8/125

Observe the above series, pattern of series is multiple by 2/5 each time.

r = (2/5)/1 = (4/25)/(2/5) = (8/125)/(4/25) = 2/5.

Therefore the above series is geometric series.

 

2) 6, 2, -2, -6

Observe the above series, pattern of series is adding negative 4 each time

d = 2 - 6 = -2 - 2 = -6 - (-2) = - 4.

Therefore the above series is arithmetic series.

3) -25, -20, -15, -10

Observe the above series, pattern of series is adding 5 each time

d = -20 - (-25) = -15 - (-20) = -10 - (-15) = 5.

Therefore the above series is arithmetic series.

 

4) 6, -3, 3/2, -3/4

Observe the above series, pattern of series is multiple by negative 1/2 each time.

r = -3/6 = (3/2)/(-3) = (-3/4)/(3/2) = - 1/2.

Therefore the above series is geometric series.