If the sum of three consecutive terms in G.P. is 216 and sum of their products in pairs is 156, find them.

Question

If the sum of three consecutive terms in G.P. is 216 and sum of their products in
pairs is 156, find them.

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Sarah 2 weeks 2021-10-07T11:25:16+00:00 1 Answer 0 views 0

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    2021-10-07T11:26:36+00:00

    Answer:

    pls mark as brianliest

    Step-by-step explanation:

    Product of three terms = 216

    (a/r) ⋅ a ⋅ a r = 216

    a3 = 63

    a = 6

    Sum of their product in pairs = 156

    (a/r) ⋅ a + a ⋅ ar + ar ⋅ (a/r) = 156

    a2 / r + a2 r + a2 = 156

    a2 [ (1/r) + r + 1 ] = 156

    a² [ (1+r²+r)/r] = 156

    a² (r²+r+1)/r = 156

    (6²/r)(r²+r+1) = 156

    (r²+r+1)/r = 156/36

    (r²+r+1)/r = 13/3

    3(r²+r+1) = 13 r

    3r² + 3r + 3 – 13r = 0

    3r² – 10r + 3 = 0

    (3r – 1)(r – 3) = 0

    3r – 1 = 0

    3r = 1

    r = 1/3

    r – 3 = 0

    r = 3

    If a = 6, then r = 1/3

    a/r = 6/(1/3) ==> 18

    a = 6

    ar = 6(1/3) ==> 2

    If a = 6, then r = 1/3

    a/r = 6/3 ==> 2

    a = 6

    ar = 6(3) ==> 18

    Hence the required three terms are 18, 6 and 2 or 2, 6, 18.

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