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If A and G be A.M. and G.M., respectivel...

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A pm sqrt((A+G )(A−G ))` .

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NCERT GUJARATI-SEQUENCES AND SERIES-EXERCISE 9.3
  1. How many terms of G.P. 3, 3^2, 3^3, … are needed to give the sum 120?

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  2. The sum of first three terms of a G.P. is 16 and the sum of the next t...

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  3. Given a G.P. with a = 729 and 7^("th") term 64, determine S7 .

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  4. Find a G.P. for which sum of the first two terms is – 4 and the fifth ...

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  5. If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively...

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  6. Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

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  7. Find the sum of the products of the corresponding terms of the sequenc...

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  8. Show that the products of the corresponding terms of the sequences a, ...

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  9. Find four numbers forming a geometric progression in which the third t...

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  10. If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...

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  11. If the first and the n^("th") term of a G.P. are a and b, respectivel...

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  12. Show that the ratio of the sum of first n terms of a G.P. to the sum o...

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  13. 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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  14. Insert two numbers between 3 and 81 so that the resulting sequence is ...

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  15. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

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  16. The sum of two numbers is 6 times their geometric mean, show that numb...

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  17. If A and G be A.M. and G.M., respectively between two positive numbers...

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  18. The number of bacteria in a certain culture doubles every hour. If the...

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  19. What will Rs 500 amounts to in 10 years after its deposit in a bank wh...

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  20. If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respect...

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