Q: if there is three AP the first term of AP is a and common difference is d then prove that S1+S2=S3
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Q: if there is three AP the first term of AP is a and common difference is d then prove that S1+S2=S3
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hope this answer will be helpful ^_^
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.