Question

Given that \( n \) number of arithmetic means are inserted between two pairs of numbers \( a,2b \) and \( 2a,b \); where \( a,b \in R \). If the \( m^{th} \) means in the two cases are the same, then the ratio \( a:b \) is equal to

• A. \( m : (n-m+1) \)
• B. \( n : (n-m+1) \)
• C. \( (n-m+1) : m \)
• D. \( (n-m+1) : n \)

Hint:

In A.P. problems, use \( T_k = a + (k-1)d \) or direct formula of inserted meansCarefully equate corresponding terms.

Answer 1

The Correct Option is A