In an A.P, if 16^(th) term is 47 and 31^(st) term is 92, then 27^(th) term is
In an A.P, if 16th term is 47 and 31st term is 92, then 27th term is
A) 86
B) 120
C) 80
D) 116
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Correct option is (C) 80
\(a_{16}=47\;\&\;a_{31}=92\)
\(\therefore a+15d=47\) ______________(1)
\(a+30d=92\) ______________(2) \((\because a_n=a+(n-1)d)\)
Subtract equation (1) from (2), we get
\((a+30d)-(a+15d)=92-47\)
\(\Rightarrow15d=45\)
\(\Rightarrow d=\frac{45}{15}=3\)
\(\therefore a=47-15d\) (From (1))
\(=47-15\times3\)
\(=47-45=2\)
\(\therefore a_{27}=a+26d\)
\(=2+26\times3\)
\(=2+78=80\)
Hence, \(27^{th}\) term of A.P. is 80.
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