The sum of the first ten terms of the geometric progression is S1 and the sum of the next ten terms (11th term to 20th term) is S2, then the common ratio will be-
(1) ± 10 S 1 S 2          (2) ± S 2 S 1              (3) ± 10 S 2 S 1             (4) S 1 S 2



Dear Student,


Given : S1=Sum of first 10 terms of a GP and S2=Sum of next10 terms of the GPTo Calculate: Common ratio in terms of S1 and S2Solution : Sum n-terms of a GP = a (rn-1)r-1So,  S1=a (r10-1)r-1.................................................1For calculting sum from 11th term to 20tha11(=a r10) will be the first term and common difference will be same and n is also 10 (from 11 to 20) S2=a11 (r10-1)r-1 S2=a r10 (r10-1)r-1 [since a11=a r10].................................................2Dividing 2 from 1S2S1=a r10 (r10-1)r-1a  (r10-1)r-1S2S1=r10r=± S2S110
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