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Find four numbers forming a geometric p...

Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the `4^(t h)`by 18.

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To solve the problem of finding four numbers that form a geometric progression (GP) given the conditions, we can follow these steps: ### Step 1: Define the terms of the GP Let the first term of the GP be \( A \) and the common ratio be \( R \). The four terms of the GP can be expressed as: - First term: \( A \) - Second term: \( AR \) - Third term: \( AR^2 \) - Fourth term: \( AR^3 \) ...
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NCERT-SEQUENCES AND SERIES-EXERCISE 9.3
  1. If the first and the nth terms of a GP are a and b respectively and if...

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

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

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

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  5. Insert two number between 3 and 81 so that the resulting sequence is ...

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  6. 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 b...

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  7. The number of bacteria in a certain culture doubles every hour. If th...

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  8. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

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  9. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respect...

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

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  11. The sum of two numbers is 6 times their geometric means, show that nu...

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  12. If the p^(t h),q^(t h)and r^(t h)terms of a GP are a, b and c, respec...

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

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

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  15. If the 4^(t h), 10^(t h)and 16^(t h)terms of a G.P. are x, y and z, r...

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

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  17. Given a G.P. with a = 729 and 7^(t h)term 64, determine S7.

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  18. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  19. How many terms of G.P. 3,3^2,3^3,dotdotdotare needed to give the sum 1...

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  20. Find the sum to indicated number of terms in each of the geometric pr...

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