4. In a sequence of positive numbers, the ratio of each term to the term immediately following it is 1 to 4. What is the rati

Question

4.
In a sequence of positive numbers, the ratio of
each term to the term immediately following it is
1 to 4. What is the ratio of the 3rd term to the 6th
term in this sequence?
(A) 1 to 4
(B) 1 to 16
(C) 1 to 64
(D) 1 to 128
(E) None of the above
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Katherine 1 month 2021-08-18T16:49:13+00:00 1 Answer 0 views 0

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    2021-08-18T16:50:49+00:00

    Answer:

    Given

    a

    n

    = 2a

    n−1

    A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

    Here, r = 2.

    In a G.P.,

    a

    n

    = a

    1

    r

    n−1

    ,

    where,

    a

    n

    is the n

    th

    term of the sequence

    a

    1

    is the 1

    st

    term of the sequence

    r

    is the common ratio

    To find the ratio of the 8

    th

    term to the 5

    th

    term,

    a

    8

    = a

    1

    2

    8−1

    a

    8

    = 2

    7

    a

    1

    a

    5

    = a

    1

    2

    5−1

    a

    5

    = 2

    4

    a

    1

    Ratio of a

    8

    to a

    5

    = 2

    7

    a

    1

    : 2

    4

    a

    1

    =

    16

    128

    : 1

    = 8 : 1

    Therefore, the ratio of the 8

    th

    term in the sequence to the 5

    th

    term is

    8 to 1

    .

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18:9+8+9*3-7:3-1*13 = ? ( )