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Is there a common ratio for the geometric sequence and what are the missing terms?

16,40,100,?,?

IS there a common ratio for the geometric sequence and what are the missing terms?

81,54,?,?,?

  • math -

    Yes, and 2.5 is the ratio. Following terms are 150, and 225.

    For the second question, try 2/3 for the ratio. 36, 24, ...
    With only two terms, one really can't say if there is a "common" ratio. There are no other pairs to compare.

  • math -

    if the given sequence is a geometric sequence, then it follows the formula
    A,n+1 = r*(A,n)
    where
    r = ratio between two consecutive terms
    A,n = the nth term
    A,n+1 = the term after A,n

    substituting the first and second term,
    40 = r*16
    r = 40/16
    r = 2.5
    to check, let's see if we would obtain 100 if we multiply 40 by the ratio=2.5
    40*2.5 = 100
    to find the next term after 100, we just multiply by the ratio,, thus the next two terms are:
    100*2.5 = 250
    250*2.5 = 625

    for the second question, if it's a geometric sequence, then it follows the formula above. thus, getting the ratio,
    54 = r*81
    r = 54/81
    r = 2/3
    to get the next three terms, we multiply the next terms by 2/3:
    54*(2/3) = 36
    36*(2/3) = 24
    24*(2/3) = 16

    hope this helps~ :)

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