arithmetic

THE SUM OF THE 2ND AND 5TH TERMS OF AN A.P IS 42.
IF THE DIFFERENCE BETWEEN THE 6TH AND 3RD TERM IS 12,
FIND THE:
COMMON DIFFERENCE,
1ST TERM,
20TH TERM.

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  1. Let
    d = the common difference
    t(n)=nth term

    t(6)-t(5)=d
    t(5)-t(4)=d
    t(4)-t(3)=d
    Add
    t(6)-t(3)=3d
    or
    3d=12
    Solve for the common difference d=4

    Sum of the 2nd and 5th terms = 42
    t(2)+t(5)
    =t(2)+(t(2)+3d)
    =2*t(2)+12 = 42
    Solve for t(2) = 15

    t(1) should be t(2)-1=15-4=11
    and
    t(20)=t(1)+19d

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  2. Explain in a simpler way please

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