Find , and between and such that , and , , are in A.P. and are in G.P.
Step 1. Find the value of and :
According to question,
…...(1)
…...(2) are consecutive terms of A.P.
and ..…..(3) are consecutive terms of G.P.
Eliminating from (1) and (2),
Step 2. Put the value of in equation (3):
is rejected because it does not lie between and
Step 3. Put the value of in equation (3):
Step 4. Put the value of in equation (2):
Thus, , and
Hence, Option ‘A’ is Correct.