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If a(1),a(2),...a(k) are in A.P. then ...

If `a_(1),a_(2),...a_(k)` are in A.P. then the equation `(S_(m))/(S_(n))=(m^(2))/(n^(2))` (where `S_(k)` is the sum of the first k terms of the A.P) is satisfied . Prove that `(a_(m))/(a_(n))=(2m-1)/(2n-1)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. The sides of a right angled triangle are in A.P. ,' show that the side...

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  2. The sum of first p terms of an A.P. is zero. Show that the sum of a n...

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  3. If a(1),a(2),...a(k) are in A.P. then the equation (S(m))/(S(n))=(m^...

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  4. If f(x)=(1)/(x^(2)), show that f(x)-f(x+1)=(2m-1)/(x^(2)(x+1)^(2)), he...

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  5. Let t(p) be the p th term of an A.P. if its n th tem is zero, show tha...

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  6. Let a,b,c,d, be four quantities such that a+c=2 b and ab+cd+ad=3bc(b n...

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  7. Does there exist a geometric progression containing 27, 8 and 12 as th...

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  8. If a=2 and e=18 , then find three numbers b,c,d betweem a and e such t...

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  9. Prove that any sequence of numbers a(1),a(2),...a(n) satisfying the co...

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  10. If (a-bx)/(a+bx)=(b-cx)/(b+cx)=(c-dx)/(c+dx) show that a,b,c , d are i...

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  11. Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+ to n terms =(n...

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  12. Show that in A.P. the sum of two terms equidistant from the begining a...

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  13. If there be m quantities in a G.P. whose common ratio is r and S(m)den...

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  14. If a,b,c are in G.P. are log(c) a , log (b) c, log(a) b are in A.P. , ...

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  15. Find the sum to n terms of the following series. 5+555+55555+...

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  16. If x in RR, solve the inequation (5x+8)/(4-x) lt2

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  17. The population of a twon at the beginning of a year is N and the figur...

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  18. Examine the validity of the following statement: If a and b ar odd i...

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  19. Show that the total number of permutations of n diferent things not mo...

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  20. A and B stand in a line with 10 other people. In how many of the perm...

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