Progression (Sequence and Series)Easy
Question
If in a GP of 3n terms, S1 denotes the sum of the first n terms, S2 the sum of the second block of n terms and S3 the sum of the last n terms, then S1, S2, S3 are in :-
Options
A.AP
B.GP
C.HP
D.None of these
Solution
Let 3n terms of G.P. are a, ar, ar2,.....,ar3n-1
Then S1 = a + ar + ar2 +....+arn-1 =
S2 = arn + arn +1 + arn+2 +....+ar2n-1 =
S3 = ar2n + ar2n+1 + ar2n+2 +....+ ar3n-1=
So, S22 = S1S3. Hence S1, S2, S3 are in G.P.
IInd method : Put the value of n.
Then S1 = a + ar + ar2 +....+arn-1 =
S2 = arn + arn +1 + arn+2 +....+ar2n-1 =
S3 = ar2n + ar2n+1 + ar2n+2 +....+ ar3n-1=
So, S22 = S1S3. Hence S1, S2, S3 are in G.P.
IInd method : Put the value of n.
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