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Answer:
Given :
To prove :
S₁ + S₃ = 2S₂
Formula :
Sum of n terms in an AP., is given by,
Solution :
Let's find the sum of n terms of each arithmetic series.
Sum of n terms of first series :
first term, a = 1
common difference, d = 1
Sum of n terms of second series :
first term, a = 1
common difference, d = 2
Sum of n terms of third series :
first term, a = 1
common difference, d = 3
we have to prove S₁ + S₃ = 2S₂
LHS = S₁ + S₃
RHS = 2S₂
LHS = RHS
S₁ + S₃ = 2S₂
Hence proved!