# 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
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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