Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

Find the partial sum Sn of the geometric sequence that satisfies the given condition?

a3 = 24, a6 = 192, n = 5

What is S5?

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  • 6 months ago

    The partial sum Sn of the geometric sequence that satisfies the given condition:

    a3 = 24, a6 = 192, n = 5

    r = 2

    6, 12, 24, 48, 96, 192, ...

    S5

    = 186

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  • 6 months ago

    The nth term of a G.P. is arⁿ⁻¹....where a is the first term and n is the nth term.

    so, 3rd term is ar² = 24 and 6th term is ar⁵ = 192

    Dividing gives:

    r³ = 192/24 => 8

    i.e. r = 2

    Hence, 4a = 24

    so, a = 6

    Hence, nth term is 6rⁿ⁻¹

    i.e. first 5 terms are: 6, 12, 24, 48 and 96

    Therefore, sum is 6 + 12 + 24 + 48 + 96 = 186

    :)>

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  • 6 months ago

    (a6)/(a3) = 192/24 = 8

    a6 = r³ * a3, so r³ = 8, and r = 2

    If a3 = 24, a1 = a3/(2²) = 24/4 = 6 = 3 * 2¹

    Now, find S5 = a1 + a2 + a3 + a4 + a5 = {Sum;i=1;5}[ 3*(2^i) ] = [3*(2^6) - 3*(2^1)]/(r - 1) = (192 - 6)/(2 - 1) = 186.

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  • 6 months ago

    If the first term is a and the ratio is r

    then a6/a3 = ar^5/ar^2 = r^3 = 192/24 = 8

    so r=2

    so a3 = 24 = ar^2 = 4a

    so a = 6

    S5 = 6(1-r^6)/(1-r) = 6(1-2^6)/(1-2) = 6 * ( 1- 64)/-1 = 6*65

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