One of the most important question of ML Aggarwal If Sn denotes the sum of the first n terms of an A.P., prove that S30=3(S20−S10)
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Arithmetic Progression Chapter 9 Question no 18
Rajan@2021Guru
If S n denotes the sum of the first n terms of an A.P., prove that S 30 =3(S 20 −S 10 )
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Let the First term of A.P=a
And common difference =d
S30=230[2a+(30−1)d]
S20=220[2a(20−1)d]
S10=210[2a+(10−1)d]
R.H.S=3[S20−S10]
=3[[220(2a+20−1)d]−[210(2a+(10−1)d]]
=3[20a+190d−10a−45d]
=15(2a+29d)
=230[2a+(30−1)d]
=S30
=L.H.S