7 th term and 14 th term of an Arithmetic sequence are 36 and 64 respectively , find the common difference and ,25th term

Question

7 th term and 14 th term of an Arithmetic sequence are 36 and 64 respectively , find the common difference and ,25th term

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Philomena 5 months 2021-08-28T08:45:26+00:00 1 Answers 0 views 0

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    2021-08-28T08:46:28+00:00

    Answer:

    (a) The common difference is 4

    (b) The 25th term is 108

    Step-by-step explanation:

    Given

    T_7 = 36

    T_{14} = 64

    Solving (a): The common difference

    The nth term of an AP is:

    T_n = a + (n -1)d

    For the 7th term, we have:

    36 = a + (7 -1)d

    36 = a + 6d

    For the 14th term, we have:

    64 =a + (14 -1)d

    64 =a + 13d

    Subtract both equations

    64 - 36 = a - a +13d-6d

    28 = 7d

    Divide by 7

    d = 4

    Solving (b): The 25th term

    First, we calculate the first term (a)

    The 7th term of the progression is:

    36 = a + 6d

    Substitute d = 4

    36 = a + 6 * 4

    36 = a + 24

    Subtract 24

    a = 36 -24

    a = 12

    The 25th term is:

    T_{25} = a  + (25 - 1)d

    T_{25} = 12  + (25 - 1)*4

    T_{25} = 12  + 24*4

    T_{25} = 108

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