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Prove that the sum of n arithmetic means...

Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them.

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JBD PUBLICATION-SEQUENCES AND SERIES-EXAMPLE
  1. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

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  2. The sums of n terms of two arithmetic progressions are in the ratio 5n...

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  3. Prove that the sum of n arithmetic means between two numbers is n time...

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  4. The digits of a positive integer having three digits are in AP and the...

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  5. If the first and the nth terms of a GP are a and b respectively and if...

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  6. How many terms of the series sqrt(3) + 3 + 3sqrt(3) +…... will make th...

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  7. Find the sum of n terms of the following sequences: 8+88+888+……………..up...

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  8. The A.M. between two positive numbers is 34 and their G.M. is 16. find...

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  9. If a be the A.M. and x, y be the two G.M's between b and c, show that ...

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  10. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  11. If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c...

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

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  13. The sum of an inifinite G.P. is 8. If the second term is 2, then find ...

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  14. Find the sum to n terms of the series 3 xx 8 + 6 xx 11 + 9 xx 14 + …

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  15. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

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

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  17. A manufacturer reckons that the value of a machine, which costs him Rs...

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  18. If A.M and G.M of two positive numbers are 13 and 12 respectively. Fin...

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  19. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  20. The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show th...

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