Question

In an A.P, if 16^th term is 47 and 31^st term is 92, then 27^th term is 

A) 86 

B) 120 

C) 80 

D) 116

Answer 1

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.

Answer 2

Correct option is C) 80