Question

If the first and the (2n-1)th terms of an A.P., G.P. and H.P. are equal and their nth terms are a, b, c respectively , then

• A. a+c = 2b
• B. a+c = b
• C. ac –b² = 0
• D. None of these

Answer 1

Answer: (C)

ac –b² = 0

Answer 2

Let α be the first and β be the (2n– 1) terms of an A.P., G.P. and H.P. Then α, a, β will be in A.P., α, b, β will be in G.P. α, c, β will be in H.P.

Hence a, b, c are respectively A. M. , G.M. and H.M. of α and β.

⇒ a =$\frac { \alpha + \beta } { 2 }$, b² = αβ and c = $\frac { 2 \alpha \beta } { \alpha + \beta }$ .Hence ac-b² =0