Show that the ratio of the sum of first ...

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from `(n + 1)^("th") " to " (2n)^("th")` term is `1/r^n` .

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NCERT TAMIL-SEQUENCES AND SERIES-EXERCISE 9.3

How many terms of G.P. 3, 3^(2), 3^(3), … are needed to give the sum 1...
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the sum of the first six terms of a GP is 9 times the sum of the first...
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If the first term of a G.P. is 729 and its 7^(th) term is 64, then the...
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Find a G.P. for which sum of the first two terms is – 4 and the fifth ...
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If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively...
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Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
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Find the sum of the products of the corresponding terms of the sequenc...
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Show that the products of the corresponding terms of the sequences a, ...
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Find four numbers forming a geometric progression in which the third t...
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If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...
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If the first and the n^("th") term of a G.P. are a and b, respectivel...
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Show that the ratio of the sum of first n terms of a G.P. to the sum o...
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If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2) = (a...
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Insert two numbers between 3 and 81 so that the resulting sequence is ...
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Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...
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The sum of two numbers is 6 times their geometric mean, show that numb...
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If A and G be A.M. and G.M., respectively between two positive numbers...
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The number of bacteria in a certain culture doubles every hour. If the...
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What will Rs. 500 amounts to in 10 years after its deposit in a bank w...
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If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respect...
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