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    • Thread Starter

    I am struggling greatly with a question on arithmetic sequences.

    10)The first term of an arithmetic sequence is six times the 5th term. The sum of the 2nd and 8th terms is 8. Find the 20th term of this sequence.

    Now first I know the nth term is a+(n-1)d. So I know the sequence of the 5th term is a+(5-1)d therefore a+4d. Knowing this, I know that the first term is 6(a+4d) therefore the first term is 6a+24d so a=6a+24d.

    Then I did the sum of the 2nd and 8th terms is 8. So for the 2nd term;
    a+(1)d therefore a+d. For the eight term a+7d. From this i worked out 2a+8d=8.
    This is where I fail. I don't know how to find the value of a or d to work out the 20th term of the sequence.


    Well, you solved it yourself.

    System of equations:
    (1) a=6a+24d => -5a=24d
    (2) 2a+8d=8

    solve (2) for d, you get d = (4-a) / 4

    Substitute that into (1) you get -5a = 24 - 6a => a = 24, d = -5

    a20 = 24 + (20-1)*(-5) = 24 - 95 = -71
    • Thread Starter

    Ah thanks a lot mate, I think I was looking to deep to find possible solutions!
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Updated: September 24, 2010
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