The sum of the first 15 terms of an arithmetic sequence is 480. Find the 8th term of the sequence.

Question

The sum of the first 15 terms of an arithmetic sequence is 480. Find the 8th term of the
sequence.

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Thành Đạt 5 years 2021-09-01T00:30:18+00:00 2 Answers 52 views 0

Answers ( )

  1. trungdung22
    0
    2021-09-01T00:31:28+00:00
    Reply

    Answer:

    32

    Step-by-step explanation:

    32

  2. Neala
    0
    2021-09-01T00:32:00+00:00
    Reply

    Given:

    The sum of the first 15 terms of an arithmetic sequence is 480.

    To find:

    The 8th term of the sequence.

    Solution:

    We have,

    S_{15}=480

    We know that, the nth term of an AP is

    a_n=a+(n-1)d

    Where, a is the first term and d is the common difference.

    Putting n=8, we get the 8th term of the sequence.

    a_8=a+(8-1)d

    a_8=a+7d

    The sum of first n terms is

    S_{n}=\dfrac{n}{2}[2a+(n-1)d]

    Where, a is the first term and d is the common difference.

    S_{15}=\dfrac{15}{2}[2a+(15-1)d]

    480=\dfrac{15}{2}[2a+14d]

    480=\dfrac{15}{2}[2(a+7d)]

    480=15(a+7d)

    Divide both sides by 15.

    \dfrac{480}{15}=a+7d

    32=a+7d

    32=a_8

    Therefore, the 8th term of the arithmetic sequence is 32.

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