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If a, b, c are three consecutive terms o...

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that `x^(b-c)timesy^(c-a)timesz^(a-b)=1`

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The correct Answer is:
`1 xx 1 = 1`
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PREMIERS PUBLISHERS-NUMBERS AND SEQUENCES-EXERCISE 2. 7
  1. Which of following sequences are in G.P. 4, 44, 444, 4444, …

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  2. Which of following sequences are in G.P. 0.5, 0.05, 0.005, …

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  3. Which of following sequences are in G.P. (1)/(3), (1)/(6), (1)/(12),...

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  4. Which of following sequences are in G.P. 1, -5, 25, -125, …

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  5. Which of following sequences are in G.P. 120, 60, 30, 18, …

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  6. Which of following sequences are in G.P. 16, 4, 1, (1)/(4), …

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  7. Write the first three terms of the G.P. whose first term and the commo...

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  8. Write the first three terms of the G.P. whose first term and the commo...

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  9. Write the first three terms of the G.P. whose first term and the commo...

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  10. In a G.P. 729, 243, 81, … find t(7)

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  11. Find x so that x+6, x+12 and x+15 are consecutive terms of Geometric P...

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  12. Find the number of terms in the following G.P. 4, 8, 16, …, 8192

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  13. Find the number of terms in the following G.P. (1)/(3), (1)/(9), (1)...

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  14. In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th te...

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  15. Find the 10th term of G.P. whose 8th term is 768 and the common ratio ...

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  16. If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

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  17. In a G.P. the product of three consecutive term is 27 and the sum of t...

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  18. A man joined a company as Assistant Manager. The company gave him a st...

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  19. Sivamani is attending an interview for a job and the company gave two ...

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  20. If a, b, c are three consecutive terms of an A.P. and x, y, z are thre...

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