If 10th term of an A.P is 0 and 42nd term is -32, then nth term is ………………
If 10th term of an A.P is 0 and 42nd term is -32, then nth term is ………………
A) 10 – n
B) 8 – n
C) 11 – n
D) 9 – n
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Correct option is (A) 10 – n
Let a & d be first term & common difference of A.P.
We have \(a_{10}=0\;\&\;a_{42}=-32\)
\(\therefore a+9d=0\) ______________(1)
& \(a+41d=-32\) ______________(2) \((\because a_n=a+(n-1)d)\)
Subtract equation (1) from (2), we get
\((a+41d)-(a+9d)=-32-0\)
\(\Rightarrow32d=-32\)
\(\Rightarrow d=\frac{-32}{32}=-1\)
\(\therefore a=-9d=-(-9)=9\) (From (1) & d = -1)
\(\therefore a_n=a+(n-1)d\)
\(=9+(n-1)d\)
\(=9-n+1\)
\(=10-n\)
Hence, \(n^{th}\) term of A.P. is 10 - n.
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