If aa is the first term of an arithmetic sequence and dd the difference between a term and its preceding term, general formula for n^(th)nth term of the arithmetic sequence is given by a+(n-1)da+(n−1)d.
As 8^(th)8th term is -20−20 and 17^th17th term is -47−47
a+(8-1)d=a+7d=-20a+(8−1)d=a+7d=−20 and a+(17-1)d=a+16d=-47a+(17−1)d=a+16d=−47.
Subtracting first equation from second, we get
9d=-47+209d=−47+20 or 9d=-279d=−27 i.e. d=-3d=−3
putting this in first we get a+7*(-3)=-20a+7⋅(−3)=−20 or a=1a=1.
Hence, n^(th)nth term of the arithmetic sequence is given by 1-3(n-1)1−3(n−1) or 4-3n4−3n
