Question

$n$ AMs are inserted between $7$ and $71$. If fifth AM is $27$, then n is equal to

• A. $17$
• B. $16$
• C. $15$
• D. None of these

Answer 1

The correct option is C $15$

Let $A_1,A_2,.............A_n$ are $n$ A.Ms inserted between $7$ and $71$.
So the common difference is $d=\frac{71-7}{n+1}=\frac{64}{n+1}$
Thus the fifth A.M will be $A_5=7+5d=7+\frac{64\times 5}{n+1}=27$ (given)
$\Rightarrow n+1=\frac{64\times 5}{20}=16\Rightarrow n=15$
Hence, option 'C' is correct.