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If the 4th, 10th and 16th terms of a G.P...

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

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The 5th, 8th and 11th terms of a G.P. are p, q and x, respectively. Show that q^2=ps .

The 4th, 7th and 10th terms of a GP. are a, b, c respectively. Show that b^2 = ac .

If the p^(th) , q^(th) and r^(th) terms of a G.P. are a, b and c, respectively. Prove that a^(q-r) b^(r-p)c^(P-q)=1 .

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If the pth , qth , rth , terms of a GP . Are x,y,z respectively prove that : x^(q-r).y^(r-p).z^(p-q)=1

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PSEB-SEQUENCES AND SERIES-EXERCISE
  1. Given a G.P. with a= 729 and 7th term 64, determine S7.

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

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

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

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

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

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  7. If the p^(th), q^(th) and r^(th) terms of a G.P. are a, b and c, respe...

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  8. If the first and the nth term of a G.P. are a and b. respectively, and...

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

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  10. If a, b, c and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^...

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

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

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

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

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

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

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

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  18. Find the sum to n terms of the series given below:- 1xx2 + 2xx3 + 3xx4...

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  19. Find the sum to n terms of the series given below:- 1xx2xx3 + 2xx3xx4 ...

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  20. Find the sum to n terms of the series given below:- 3xx1^2+5xx2^2+7xx3...

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