A sequence is formed from an inductive relationship: Un+1=2Un+5. given that U1=2, find the first four terms of the sequence.?

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  • 6 months ago

    A sequence is formed from an inductive relationship: U n + 1 = 2 U n + 5.

    Given that U 1 = 2, the first four terms of the sequence:

    2, 9, 23, 51

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  • JOHN
    Lv 7
    6 months ago

    Un+1 = 2Un +5 means double the previous number and add 5.

    Starting with 2: 2 x 2 +5 = 9

    Next: 2 x 9 + 5 = 23

    Next 2 x 23 + 5 = 51

    The 1st four terms are 2, 9, 23, 51.

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  • 6 months ago

    This is one of those cases where we need a clear notation for subscripts to make sense of that equation.

    I will use the format

    X[k]

    to indicate k is a subscript of X.

    In this notation, I believe the equation for the relationship is meant to be

    U[n+1] = 2 U[n] + 5

    (That is, the +1 is inside a subscript and the +5 is not.)

    So we would have

    U[1] = 2

    U[2] = 2 U[1] + 5 = 4 + 5 = 9

    U[3] = 2 U[2] + 5 = 18 + 5 = 23

    U[4] = 2 U[3] + 5 = 46 + 5 = 51

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