Question

If $n$ arithmetic means are inserted between $1$ and $31$ such that ratio of first and $n^{th}$ mean is $3:29$, then what is the value of $n$?

• A. $10$
• B. $14$
• C. $18$
• D. $23$

Answer 1

Answer: (B)

$14$

first mean $=1+d$

$n^{th}$ mean $=1+nd$

$ratio=\frac{3}{29}$
$\frac{1+d}{1+nd}=\frac{3}{29}$...........(1)

$31=1+(n+1)d$ .........................(2)

solving equations (1) and (2)

$n=14$