Question

If the first and $(2n+1{)}^{th}$ terms of an A.P; G .P and H.P are equal and their $(n+1{)}^{th}$ terms are $a,bandc$ respectively , then

• A. $a>b>c$
• B. $ac=b^2$
• C. $a+b=c$
• D. $a+c=b$

Answer 1

The correct option is B $ac=b^2$

Let $T_1$ & $T_{2n+1}$ are A & B
Between there terms A+b; $T_n=a,b,c$ when series are in A.P, G.P & H.P. respectively.
$\Rightarrow a=\frac{A+B}{2},b=\sqrt{AB},c=\frac{2AB}{A+B}$
$\Rightarrow b^2=ac$