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20 January, 06:18

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 =

+5
Answers (2)
  1. 20 January, 08:41
    0
    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
  2. 20 January, 09:12
    0
    Answers:

    1: 2,3,6

    2:

    a. 3, 0.2

    b. 5, 2

    c. 1/2, 20
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