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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) . y^(c-a).z^(a-b)=1`

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ICSE-SEQUENCE AND SERIES -CHAPTER TEST
  1. If a, b, c are three consecutive terms of an A.P. and x,y,z are three ...

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  2. Write down the first five terms of the sequence, whose nth term is (-1...

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  3. If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, fin...

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  4. Find the sum of all natural numbers between 100 and 1000 which are mul...

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  5. How many terms of the A.P., -6,(-11)/(2),-5 ... are needed to give the...

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  6. Determine the sum of the first 35 terms of an A.P. if a(2), = 2 and a(...

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  7. If the first term of an A.P. is 2 and the sum of first five terms is e...

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  8. Insert 3 arithmetic means between 2 and 10.

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  9. Find 12th term of a G.P. whose 8th term is 192 and the common ratio is...

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  10. The first term of a G.P. is 1. The sum of the third and fifth terms is...

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  11. The sum of first three terms of a G.P. is (39)/(10) and their product ...

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  12. The sum of some terms of a G.P. is 315 whose first term and the common...

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  13. Find the sum of the series 0.6 +0.66 +0.666+ ... to the n terms

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  14. The sum of an infinite series is 15 and the sum of the squares of thes...

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  15. Insert three geometric means between 1 and 256.

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  16. In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2...

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  17. Find the sum to n terms of the series 3.8 +6.11 +9.14 + ...

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  18. Find the sum 5^(2)+ 6^(2) + 7^(2) + ... + 20^(2).

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  19. If in a geometric progression consisting of positive terms, each term ...

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  20. If the first term of an infinite G.P. is 1 and each term is twice the ...

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  21. If fifth term of a G.P. is 2, then the product of its first 9 terms is

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