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14 June, 03:29

The fifth and tenth term of an A. P are 8 and - 7 respectively. Find the 100th and 500th term of the A. P

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  1. 14 June, 06:21
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    An arithmetic sequence can be expressed as:

    a (n) = a+d (n-1), where a (n) is the value of the nth term, a is the initial term, d is the common difference, and n is the term number ... we are given to terms ...

    8=a+d (5-1) and - 7=a+d (10-1) so

    8=a+4d and - 7=a+9d

    So if we get the difference of these two equations we have:

    15=-5d, so d=-3

    We again use one of the original equations to solve for the first term and using the common difference d that we just found ...

    8=a-3 (5-1)

    8=a-12, so a=20, so are sequence has the rule:

    a (n) = 20-3 (n-1) or more neatly:

    a (n) = 23-3n so

    a (100) = - 277

    a (500) = - 1477
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