Question

Let $A_1,A_2,...A_{n}and{H}_1,H_2,...H_n$ are $n$ $A.Ms$ & $H.Ms$ between the two quantities $a$ & $b$ $(a,b>0)$ respectively. On the basis is of above information answer the following questionsLet $P$ be the first mean between $a$ & $b$, then $P$ equals

• A. $\frac{na-b}{n+1}$
• B. $\frac{na+b}{n+1}$
• C. $\frac{nb+a}{n+1}$
• D. $\frac{nb-a}{n+1}$

Answer 1

The correct option is B $\frac{na+b}{n+1}$

As $a,A_1,A_2,....A_n,b\in A.P.$

$\therefore d=\frac{b-a}{n+1}$

$\therefore P=A_1=a+d=a+\frac{b-a}{n+1}=\frac{na+b}{n+1}$

Hence choice, $\left(B\right)$ is correct.