find the next 5 terms and 14th term of an AP root2, root8, root18​

Question

find the next 5 terms and 14th term of an AP root2, root8, root18​

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Serenity 2 months 2021-07-30T02:38:17+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-30T02:39:36+00:00

    Given:

    • An A.P √2, √8, √18

    To Find:

    • Next five Terms and 14th term

    Formula Used:

    • {\boxed{\bf{a_n=a+(n-1)d}}}

    Solution:

    Firstly,

    • √2
    • √8 = 2√2
    • √18 = 3√2

    So, the A.P can also be √2, 2√2, 3√3

    Here,

    • a = √2
    • d = 2√2 – √2 = √2

    For next five Terms,

    • 4th term = 3√2 + √2 = 4√2 = √32
    • 5th term = 4√2 + √2 = 5√2 = √50
    • 6th term = 5√2 + √2 = 6√2 = √72
    • 7th term = 6√2 + √2 = 7√2 = √98
    • 8th term = 7√2 + √2 = 8√2 = √128

    Hence, The next five Terms of the given A.P is 72, 50, 72, 98 and 128.

    Now, For 14th term of an A.P,

    \bf :\implies\:a_n=a+(n-1)d

    Here, n = 14

    \sf :\implies\:a_14=\sqrt{2}+(14-1)\times \sqrt{2}

    \sf :\implies\:a_14=\sqrt{2}+13 \sqrt{2}

    \sf :\implies\:a_14=14\sqrt{2}

    \bf :\implies\:a_14=\sqrt{392}

    Hence, The 14th Term of an A.P is 392.

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    0
    2021-07-30T02:39:57+00:00

    Answer:

    The next five terms for an AP is

     \sqrt{32}  \\  \sqrt{50}  \\  \sqrt{72}  \\  \sqrt{98}  \\  \sqrt{128}

    Step-by-step explanation:

    the \: 14 \:th \: term \: of \: an \: ap \: is \:  \sqrt{392}

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