Question

If $m$ arithmetic means are inserted between $1$ and $31$ so that the ratio of the $7th$ and $(m-1)th$ means is $5:9$, then the value of $m$ is

• A. $9$
• B. $11$
• C. $13$
• D. $14$

Answer 1

The correct option is D $14$

m arithmetic mean are inserted between $1$ and $31$

$\frac{7^{th}mean}{(m-1{)}^{th}mean}=\frac{5}{9}\frac{1+7d}{1+(m-1)d}=\frac{5}{9}=>9+63d=5+5(m-1)d4=5md-68d1+(m-1)d=31md-d=30-5\times 2=>-73d=-146d=2m=14$