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25 August, 22:11

The arithmetic sequence a1 is defined by the formula:

a1 = 4

a1=ai-1 + 11

Find the sum of the first 650 terms in the sequence.

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Answers (1)
  1. 25 August, 22:34
    0
    2,322,775

    Step-by-step explanation:

    Given a1 = 4 and ai = ai-1 + 11

    when i = 2

    a2 = a2-1+11

    a2 = a1+11

    a2 = 4+11

    a2 = 15

    when i = 3

    a3 = a2+11

    a3 = 15+11

    a3 = 26

    The sequence formed by a1, a2, a3 ... is am arithmetic sequence as shown;

    4, 15, 26 ...

    Sum of nth term of an arithmetic sequence = n/2{2a + (n-1) d}

    a is the first term = 4

    d is the common difference = 15-4 = 26-15 = 11

    n is the number of terms.

    Since we are to find the sum of the first 650 terms in the sequence, n = 650

    S650 = 650/2{2 (4) + (650-1) 11}

    S650 = 325{8 + (649) 11}

    S650 = 325 (8+7,139)

    S650 = 325*7147

    S650 = 2,322,775
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