Question

Q: if there is three AP the first term of AP is a and common difference is d then prove that S1+S2=S3​

Answer 1

hope this answer will be helpful ^_^

Answer 2

Step-by-step explanation:

Formula of summation of an A.P: ,

where  = Summation till n terms.

                                 a = First term of sequence

                                 d = Common Difference.

Now, using this formula, we get 

                               S1 = ,

                               S2 = , &

                               S3 = .

Therefore, to get the desired equation, we add S1 and S3.

                    ∴ S1 + S3 = 

                                     = 

                                     = 

                                     = 

                                     = 2(S2).

∴, S1 + S3 = 2(S2).

Hence proved.