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14 April, 04:21

In an AP the seventh term is 38 and the twelfth term is 63. What is the sum of the first twenty terms?

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  1. 14 April, 06:13
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    Answer: 1110

    Step-by-step explanation:

    For an arithmetic progression, the nth term is gotten by using the formula:

    = a + (n-1) d

    Therefore,

    7th term = a + 6d = 38 ... equation i

    12 term = a + 11d = 63 ... equation ii

    Subtract equation i from ii

    (a + 6d) - (a + 11d) = 38 - 63

    -5d = - 25

    d = 25/5

    d = 5

    Since d = 5

    From a + 6d = 38

    a = 38 - 6d

    a = 38 - (6*5)

    a = 38 - 30

    a = 8

    The sum of the first 20 terms will be:

    = n/2[2a + (n-1) d]

    = 20/2[ (2*8) + (20-1) 5]

    = 10[16 + (19 * 5) ]

    = 10 (16+95)

    = 10 (111)

    = 1110
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