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If `p^(th), q^(th), r^(th) and s^(th)` terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

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KUMAR PRAKASHAN-SEQUENCE AND SERIES-Testbook Illustrations for Practice Work
  1. If the sum of n terms of an A.P. is nP+1/2n(n-1)Q , where P and Q are...

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  2. The sum of n terms of two arithmetic progressions are in the ratio (3n...

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  3. The income of a person is Rs 3,00,000 in the first year and he receive...

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  4. Example 8 Insert 6 numbers between 3 and 24 such that the resulting se...

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  5. Find the 10^(th) and n^(th) terms of the G.P . 5, 25,125 ................

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  6. Which term of the G.P., 2,8,32, ... up to n terms is 131072 ?

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  7. In a GP the 3rd term is 24 and 6th term is 192. Find the 10th term.

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  8. Find the sum of first n terms and the sum of first 5 terms of the geom...

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  9. How many terms of the G.P.3,(3)/2,3/4 ..........are needed to give the...

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  10. The sum of first three terms of a G.P. is 13/12 and their product is –...

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  11. Find the sum of the sequence 7, 77, 777, 7777, ... to n terms.

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  12. A person has 2 parents, 4 grandparents, 8 great grandparents, and so o...

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  13. Insert three numbers between 1 and 256 so that the resulting sequence ...

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  14. If A.M. and G.M. of two positive numbers a and b are 10 and 8, respect...

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  15. Find the sum to n terms of the series : 5+11+19+29+41..........

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  16. Find the sum to n terms of the series whose n^("th") term is n (n+3).

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  17. If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, the...

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  18. If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y...

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  19. If a, b, c, d and p are different real numbers such that (a^2 + b^2 + ...

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  20. If p,q,r are in G.P. and the equations, px^(2) + 2qx + r = 0 and dx^2+...

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