Mathematics

Question

find the sum of the following gp:6,12,24,......to 10term and 1,-1/2,1/4,1/8,1/16.........to 20term​

1 Answer

  • Answer:

    Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138

    S'ₙ =2.52

    Step-by-step explanation:

    sum of this sequence: Sₙ = A₁ x (1 - pⁿ) / (1 - p)

    Sₙ: sum of n terms

    A₁: initial value 6

    p: common ratio 2

    n: terms 10

    Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138

    Is there any mistake in the 2nd question - about the common ratio (-1/2)?

    S'ₙ =1 + (-1/2) + 1 x (1 - (1/2)¹⁸)) / (1 - (1/2)) = 1/2 + 2 x  (1 - (1/2)¹⁸)

    S'ₙ = 1/2 + 2 x (1 - 1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52

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