Sum of a geometric series to n terms with common ratio r is given by
S(n)=a(r^n-1)/(r-1).
1. Form the equation:
S(20)/S(10)=244 (given condition)
2. Cancel out the common factor a and (r-1).
3. set u=r^10, then r^20=r^2.
4. solve the resulting quadratic in u.
5. Back-substitute u=r^10, or
r=the tenth root of each solution for u.
6. Substitute r back into the original condition (1) above to validate solution. Reject solutions that do not satisfy condition (1) above.
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the sum of first 20 terms of a G.P is 244 times the sum of its first 10 terms. the common ration is ?
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