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19 November, 02:45

The arithmetic sequence a_ia

i



a, start subscript, i, end subscript is defined by the formula:

a_1 = 5a

1



=5a, start subscript, 1, end subscript, equals, 5

a_i = a_{i - 1} + 2a

i



=a

i-1



+2a, start subscript, i, end subscript, equals, a, start subscript, i, minus, 1, end subscript, plus, 2

Find the sum of the first 700700700 terms in the sequence.

+3
Answers (1)
  1. 19 November, 05:10
    0
    492,800

    Step-by-step explanation:

    Given ith term of an arithmetic sequence as shown:

    ai = a (i-1) + 2

    and a1 = 5

    When i = 2

    a2 = a (2-1) + 2

    a2 = a1+2

    a2 = 5+2

    a2 = 7

    When i = 3

    a3 = a (3-1) + 2

    a3 = a2+2

    a3 = 7+2

    a3 = 9

    It can be seen that a1, a2 and a3 forms an arithmetic progression

    5,7,9 ...

    Given first term a1 = 5

    Common difference d = 7-5 = 9-7 = 2

    To calculate the sum of the first 700 of the sequence, we will use the formula for finding the sum of an arithmetic sequence.

    Sn = n/2{2a1 + (n-1) d}

    Given n = 700

    S700 = 700/2{2 (5) + (700-1) 2}

    S700 = 350{10+699 (2) }

    S700 = 350{10+1398}

    S700 = 350*1408

    S700 = 492,800

    Therefore, the sum of the first 700 terms in the sequence is 492,800
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