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If-S-1-S-2-S-3-be-the-sum-of-n-2n-3n-terms-respectively-of-an-AP-then-




Question Number 11977 by 786786AM last updated on 08/Apr/17
If  S_1 , S_2 , S_3  be the sum of n, 2n, 3n terms  respectively of an AP, then
IfS1,S2,S3bethesumofn,2n,3ntermsrespectivelyofanAP,then
Answered by ajfour last updated on 08/Apr/17
S_1 =(n/2)[2a+(n−1)d]  S_2 =n[2a+(2n−1)d]  S_3 =((3n)/2)[2a+(3n−1)d]  S_2 −2S_1 = n^2 d  S_3 −3S_1 =((3n)/2)(2nd)=3n^2 d  ⇒ S_3 −3S_1 =3(S_2 −2S_1 )  or  S_3 =3(S_2 −S_1 ) .
S1=n2[2a+(n1)d]S2=n[2a+(2n1)d]S3=3n2[2a+(3n1)d]S22S1=n2dS33S1=3n2(2nd)=3n2dS33S1=3(S22S1)orS3=3(S2S1).

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