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1 September, 01:42

The 10th term in the sequence is 2560 what is the 11th term in the sequence

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  1. 1 September, 01:50
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    Full Question:

    The 4th term of a g. p. is 40 and the 10th term in the sequence is 2560, what is the 11th term in the sequence?

    Answer:

    the 11 the term is 5120

    Step-by-step explanation:

    Given

    Geometry Progression

    4th term = 40

    10th term = 2560

    Required

    11 term.

    The nth term of a geometric sequence is calculated as follows

    Tₙ = arⁿ⁻¹

    For the 4th term, n = 4 and Tₙ = 40

    Substitute these in the given formula; this gives

    40 = ar⁴⁻¹

    40 = ar³. - -;; equation 1

    For the 10th term, n = 10 and Tₙ = 2560

    Substitute these in the given formula; this gives

    2560 = ar¹⁰⁻¹

    2560 = ar⁹. - -;; equation 2

    Divide equation 2 by 1. This gives

    2560/40 = ar⁹/ar³

    64 = r⁹/r³

    From laws of indices

    64 = r⁹⁻³

    64 = r⁶

    Find 6th root of both sides

    (64) ^1/6 = r

    r = (2⁶) ^1/6

    r = 2

    Substitute r = 2 in equation 1

    40 = ar³. Becomes

    40 = a * 2³

    40 = a * 8

    40 = 8a

    Divide both sides by 8

    40/8 = 8a/8

    5 = a

    a = 5.

    Now, the 11 term can be solved using Tₙ = arⁿ⁻¹ where n = 11

    So,

    Tₙ = arⁿ⁻¹ becomes

    Tₙ = 5 * 2¹¹⁻¹

    Tₙ = 5 * 2¹¹⁻¹

    Tₙ = 5 * 2¹⁰

    Tₙ = 5 * 1024

    Tₙ = 5120.

    Henxe, the 11 the term is 5120
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