Geometric Progression

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  • Q1

    Sum to n terms of the series:
    7 + 77 + 777 + ...

    Marks:2
    Answer:

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  • Q2

    Find the sum of the following series:
    243 + 324 + 432 +....... to n terms.

    Marks:3
    Answer:

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  • Q3

    Find the GP whose 4th term is 54 and the 7th term is 1458.

    Marks:1
    Answer:

    We have,

    t4 = ar3 = 54 ...(1)

    t7 = ar6 = 1458 ...(2)

    Dividing (2) from (1), we get

    r3 = 1458/54 = 27

    or r = 3

    Therefore, from (1), we get
    27a = 54

    or a = 2.

    Hence, the GP is 2, 6, 18, 54,...

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  • Q4

    Find the nth term of the sequence 2, 6, 18, ...

    Marks:1
    Answer:

    Here a = 2, r = 6/2 = 3.

    Therefore, nth term Tn = arn-1 = 2 x 3n-1.

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  • Q5

    The first three terms of a geometric sequence are 48, 24 and 12. what are the common ratio and fourth term of this sequence?

    Marks:1
    Answer:

    To find the common ratio, divide any term by its predecessor.

    24/48 = 1/2 or 12/24 = 1/2

    Therefore, the common ratio is 1/2

    Now we have to find the fourth term for that we need to multiply the third term by the common ratio 12 x 1/2 = 6.

    Hence, the fourth term is 6.

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