Which of the following are geometric series? Select all that apply.

0.2 + 0.3 + 0.4 + 0.5

0.2 + 0.6 + 1.8 + 5.4

2 + 10 + 50 + 250

2 + 4 + 6 + 8

22 + 20 + 18 + 16

20 + 10 + 5 + 2.5

Identify the value of r and a1 for each geometric series.

0.2 + 0.6 + 1.8 + 5.4

r =

a1 =

2 + 10 + 50 + 250

r =

a1 =

20 + 10 + 5 + 2.5

r =

a1 =

Answers:

1: 2,3,6

2:

a. 3, 0.2

b. 5, 2

c. 1/2, 20

second, third, and sixth options are geometric series

Step-by-step explanation:

Consider analyzing the quotient of two consecutive terms of the series a term divided the one preceding it - (do such for all terms listed) and see if there is a "common ratio" appearing for them.

In the case: 0.2 + 0.6 + 1.8 + 5.4

do: 0.6/0.2 = 3 1.8/0.6 = 3 5.4/1.8 = 3

therefore 3 is the "common ratio" - -> r = 3

and the first term of the series is: a1 = 0.2

In the case: 2 + 10 + 50 + 250

do: 10/2 = 5 50/10 = 5 250/50 = 5

therefore 5 is the "common ratio" - -> r = 5

and the first term of the series is: a1 = 2

In the case: 20 + 10 + 5 + 2.5

do: 10/20 = 0.5 5/10 = 0.5 2.5/5 = 0.5

therefore 0.5 is the "common ratio" - -> r = 0.5

and the first term of the series is: a1 = 20