Question

If $n$ arithmetic means are inserted between $2$ and $38$ If third arithmetic mean is $14$ then $n$ is equal to

• A. $9$
• B. $7$
• C. $8$
• D. $10$

Answer 1

The correct option is C $8$

$2,A_1,A_2,.....A_n,38$

Now,

First term $=2$

Common difference $=d\left(\text{Say}\right)$

Total no. of terms $=n+2$

$A_3=14\left(\text{Given}\right)$

$14=2+3d$

$\Rightarrow d=\frac{12}{3}=4$

Last term $=38$

$a+((n+2)-1)d=38$

$2+(n+1)4=38$

$n+1=\frac{38-2}{4}$

$\Rightarrow n=9-1=8$