Find the 5th term of the arithmetic sequence with a7=25 and a3 =55.

Question

Find the 5th term of the arithmetic sequence with a7=25 and a3 =55.

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Thu Nguyệt 6 months 2021-07-28T02:55:33+00:00 1 Answers 6 views 0

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    2021-07-28T02:57:12+00:00

    Answer:

    a₅ = 40

    Step-by-step explanation:

    The n th term of an arithmetic sequence is

    a_{n} = a₁ + (n – 1)d

    where a₁ is the first term and d the common difference

    Given a₇ = 25 and a₃ = 55 , then

    a₁ + 2d = 55 → (1)

    a₁ + 6d = 25 → (2)

    Subtract (1) from (2)  term by term to eliminate a₁, then

    4d = – 30 ( divide both sides by 4 )

    d = – 7.5

    Substitute d = 7.5 into (1)

    a₁ + 2(- 7.5) = 55

    a₁ – 15 = 55 ( add 15 to both sides )

    a₁ = 70

    Thus

    a₅ = 70 – 7.5(4) = 70 – 30 = 40

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