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If (1)/(x+y),(1)/(2y),(1)/(y+t) are in A...

If `(1)/(x+y),(1)/(2y),(1)/(y+t)` are in A.P . Prove that x,y,t are in G.P.

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PATHFINDER-SEQUENCES AND SERIES-QUESTION BANK
  1. If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...

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  2. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx) (x+-0) then show a,b,c an...

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  3. Sum to n term .7+.77+.777.......

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  4. The difference between any two consecutive interior angles of a polygo...

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  5. The sum of n term of three A.P are S1,S2,and S3. The frist term of eac...

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  6. If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N ...

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  7. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

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  8. Find the sum of the infinite series 1+(2)/(3)+(3)/(3^2)+(4)/(3^3)+.......

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  9. Find the sum of n terms of the series 3+7+14+24+37+.....

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  10. If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are co...

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  11. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  12. Evaluate sum(k=1)^11(2+3^k)

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

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

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  15. Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2...

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  16. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3 , respectiv...

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  17. The p th ,q th and r th terms of an A.P are a,b,c respectively. Show t...

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  18. A man saves Rs 32 during frist year Rs.36 in the next year and Rs.40 i...

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  19. If (1)/(x+y),(1)/(2y),(1)/(y+t) are in A.P . Prove that x,y,t are in G...

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  20. If one A.M 'a' and two GM's p and q be inserted between any two given...

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