Find a probable next term for the sequence 9,20,39,72,125,204,315

Question

Find a probable next term for the sequence 9,20,39,72,125,204,315

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niczorrrr 4 years 2021-07-28T05:53:06+00:00 1 Answers 6 views 0

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    2021-07-28T05:54:29+00:00

    Answer:

    464

    Step-by-step explanation:

    The first term is 9.

    The difference between the second and first term = 20 – 9 = 11

    The difference between the third and second term = 39 – 20 = 19

    The difference between the fourth and third term = 72 – 39 = 33

    The difference between the fifth and fourth term = 125 – 72 = 53

    The difference between the sixth and fifth term = 204 – 125 = 79

    The difference between the seventh and sixth term = 315 – 204 = 111

    The differences are 11, 19, 33, 53, 79, 111

    From the difference: 19 – 11 = 8, 33 – 19 = 14, 53 – 33 = 20, 79 – 53 = 26, 111 – 79 = 32

    We can see from the first difference (8), if we add 6 we get 14, if we add another 6 we get 20, if we add 6 we get 26, if add 6 we get 32

    We get the eight term using:

    32 + 6 = 38

    let x be the difference between the eight term and the seventh term, hence:

    x – 111 = 38

    x = 111 + 38

    x = 149

    Therefore:

    eighth term – seventh term = 149

    eighth term – 315 = 149

    eighth term = 149 + 315

    eighth term = 464

    The next probable term is 464

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