Question

The sum of the two numbers is $2\frac{1}{6}$. An even numbers of arithmetic means are inserted between them and their sum exceeds their number by 1. Then the number of means inserted is-

• A. 6
• B. 8
• C. 12
• D. 15

Answer 1

The correct option is C 12

Let the two numbers be a and b
given $a+b=\frac{13}{6}$
and A.M.'s are $A_1,A_2,.....A_{2n}$ inserted between a and b.
Here a, $A_1,A_2,.....,A_{2n}$, b are A.P. then given condition
$A_1+A_2+.....+A_{2n}=2n+1$

or $(a+A_1+A_2+.....+A_{2n}+b)-(a+b)=2n+1$

or $\frac{(2n+2)}{2}(a+b)-(a+b)=2n+1$
or $n(a+b)=2n+1$
or $13n=12n+6$
or $n=6$
Hence number of means are 12.