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If a,b,c,d,e are five numbers such that ...

If a,b,c,d,e are five numbers such that a,b,c are in A.P., b,c,d are in G.P. and c,d, e ar in H.P. prove that a,c,e are in G.P.

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RESONANCE ENGLISH-SEQUENCE & SERIES -SELF PRACTICE PROBLEMS
  1. Find the sum of first 16 terms of an A.P. a (1), a (2), a(3)……….. If...

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  2. There are n A.M. s between 3 and 29 such that 6th mean : (n - 1) th me...

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  3. For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)),...

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  4. about to only mathematics

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  5. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

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  6. A G.P. consist of 2n terms. If the sum of the terms occupying the odd ...

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  7. If the continued product of three numbers in G.P. is 216 and the sum o...

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  8. 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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  9. If a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3...

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  10. If a,b,c,d,e are five numbers such that a,b,c are in A.P., b,c,d are i...

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  11. If the ratio of H.M. between two positive numbers 'a' and 'b' (a gt b)...

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  12. (i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c)...

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  13. If a,b,c ,d are in H.P., then show that ab + bc + cd =3ad

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  14. If 4 + (4 +d)/( 5) + (4 + 2d)/(5 ^(2)) ……….=1, then find d.

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  15. Evaluate :1 + 3x + 6x ^(2) + 10 x ^(3)+……. upto infinite term, whre |x...

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  16. Sum to n terms of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^...

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  17. Sum to n terms the series (3)/(1 ^(2) . 2 ^(2)) + (5)/( 2 ^(2) . 3 ^...

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  18. Sum to n terms the series 1 + (1+ 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4)...

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  19. Sum to n terms the series 4 + 14 + 30 + 52+ 82+ 114+.........

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  20. If sum (r =1) ^(n ) T (r) = (n +1) ( n +2) ( n +3) then find sum ( r ...

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