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16 April, 02:18

2. Find the next three terms in the sequence.

2.5, 5, 10, 20, ...

A 40, 80, 160

B 25, 30, 35

C 50, 100, 200

D 30, 40, 50

+5
Answers (1)
  1. 16 April, 02:27
    0
    A 40, 80, 160

    Step-by-step explanation:

    Given:

    2.5, 5, 10, 20, ...

    geometric sequence has a constant ratio r and is given by

    an=a1r (r) ^ (n-1)

    where

    an=nth term

    r=common ratio

    n=number of term

    a1=first term

    In given series:

    a1=2.5

    r = a (n+1) / an

    r=5/2.5

    r=2

    Now computing next term a5

    a5=a1 (r) ^ (n-1)

    = 2.5 (2) ^ (4)

    = 40

    a6=a1 (r) ^ (n-1)

    = 2.5 (2) ^ (5)

    =80

    a7=a1 (r) ^ (n-1)

    = 2.5 (2) ^ (6)

    =160

    So the sequence now is 2.5, 5, 10, 20,40, 80, 160!
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