If are the sum of terms respectively of an arithmetic progression, then
Finding the relations between terms:
Step 1:Solve using sum of nth term formula of an AP
We know that formula to find the sum of an A.P is
, where is the sum of the terms, is the initial term, and is a common difference.
Then with terms will be
For terms, the sum will be,
For terms, the sum will be,
Step 2: Solve the equations to find relationship between the above three sums
Subtract , then we get
Now, if we multiply both the sides , we have
From ,
Hence, the correct option is (C).