A) 21
B) 25
C) 31
D) 27
Correct Answer: D
Solution :
(d): Suppose, there are n terms in the given AP. Given, first term a = 18, common difference \[d=15\frac{1}{2}-18=\frac{31}{2}-18=\frac{31-36}{2}=\frac{-5}{2}\] Then, nth term \[{{a}_{n}}=-47\Rightarrow a+(n-1)\left( \frac{-5}{2} \right)=-47\] \[[\because a+(n-1)d={{a}_{n}}]\] \[\Rightarrow 18+(n-1)\left( \frac{-5}{2} \right)=-47\] \[\Rightarrow \left( \frac{-5}{2} \right)(n-1)=-47-18=-65\] \[\Rightarrow (n-1)=-65\times \frac{-2}{5}=-13\times -2=26\] \[\Rightarrow n=26+1=27\]
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