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22 July, 04:47

Find the sum of the arithmetic sequence. 3,5,7,9, ...,21

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  1. 22 July, 06:13
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    The sum of any arithmetic sequence is the average of the first and last terms times the number of terms.

    Any term in an arithmetic sequence is:

    a (n) = a+d (n-1), where a=initial term, d=common difference, n=term number

    So the first term is a, and the last term is a+d (n-1) so the sum can be expressed as:

    s (n) (a+a+d (n-1)) (n/2)

    s (n) = (2a+dn-d) (n/2)

    s (n) = (2an+dn^2-dn) / 2

    However we need to know how many terms are in the sequence.

    a (n) = a+d (n-1), and we know a=3 and d=2 and a (n) = 21 so

    21=3+2 (n-1)

    18=2 (n-1)

    9=n-1

    10=n so there are 10 terms in the sequence.

    s (n) = (2an+dn^2-dn) / 2, becomes, a=3, d=2, n=10

    s (10) = (2*3*10+2*10^2-2*10) / 2

    s (10) = (60+200-20) / 2

    s (10) = 240/2

    s (10) = 120
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