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CGP EDU Academic Team
Published on: August 14, 2026
If a and b are two non-zero numbers. If p be the first of the n arithmetic means inserted between a and b while q is the first of n harmonic inserted between a and b show that p = 
, q = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. Let the arithmetic means inserted be x 1 , x 2 , ….., x n (x 1 = p) then b = a + (n +1) d
⇒ d = 
⇒ x 1 = a + d = 
To prove the other part let h 1 , h 2 , ….. , h n be n harmonic means (h 1 = q) inserted between a and b then 
, 
, 
, ….., 
, 
must be in A.P. and therefore 
= 
+ (n +1) d
⇒ d = 
= 
Now 
= 
= 
+ 
which easily gives q = 
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