Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

a quadratic sequence has the first three terms 5 13 and 25. find the nth term of the sequence?

how do i do this? everytime i try i get it wrong. online class is not helping 

2 Answers

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  • sepia
    Lv 7
    1 month ago

    The nth term is an² + bn + c

    The first three terms 5, 13, and 25. 

    a + b + c = 5

    4a + 2b + c = 13

    9a + 3b + c = 25

    Solution:

    a = 2, b = 2, c = 1

    The nth term is 2n² + 2n + 1

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  • 1 month ago

    The nth term is an² + bn + c

    When n = 1 we have a value of 5 so,

    a + b + c = 5....(1)

    With n = 2 we have 13 so,

    4a + 2b + c = 13...(2)

    And with n = 3 we have:

    9a + 3b + c = 25...(3)

    (2) - (1) => 3a + b = 8...(4)

    (3) - (2) => 5a + b = 12...(5)

    (5) - (4) => 2a = 4

    Hence, a = 2

    Then, b = 2 => c = 1

    Therefore, nth term is 2n² + 2n + 1

    This checks out for n = 1, 2 and 3

    :)>

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