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If a,b,c are in A.P., show that (a-c)^(2...

If a,b,c are in A.P., show that `(a-c)^(2)=4(b^(2)-ac)`.

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FULL MARKS-NUMBERS AND SEQUENCES-ADDITIONAL QUESTION SOLVED (II.ANSWER THE FOLLOWING)
  1. Show that the square of any positive integer of the form 3m or 3m + 1 ...

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  2. If the H.C.F. of 65 and 117 is expressible in the form of 65m-117, the...

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  3. Compute x such that 5^(4) -= x (mod 8)

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  4. The first term of an A.P. is 6 and the common difference is 5. Find th...

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  5. Which term of the arithmetic sequence 24,23 (1/4), 21 (3/4),….. is 3?

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  6. Find n so that the nth terms of the following two A.P.’s are the same....

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  7. If a,b,c are in A.P., show that (a-c)^(2)=4(b^(2)-ac).

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  8. Find the sum of the first 30 terms of an A.P. whose nth term is 3 + 2n...

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  9. Find the sum of the firt 40 terms of the series 1^(2) -2^(2) + 3^(2) -...

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  10. The sum of first n terms of a certain series is given as 3n^(2)-2n. Sh...

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  11. If a clock strickes once at 1 o'clock, twice at 2o'clock, thrice at 3 ...

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  12. If the 4th and 7th term of Geometrics Progressions are 54 and 1458 res...

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  13. Which term of the geometric sequence, (i) 5,2,4/5,8/25,….. Is 128/15...

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  14. How many consecutive terms starting from the first term of the scries ...

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  15. A geometric series consists of four terms and has a positive common ra...

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  16. Suppose that five people are ill during the first week of an epidemic ...

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  17. A gardener wanted to reward a boy for his good deeds by giving some ma...

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  18. Find the value of k if 1^(3) + 2^(3) + 3^(3) +…….. + k^(3) =2025

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  19. If 1^(3) + 2^(3) + 3^(3) + ……. + k^(3) =8281, then find 1+2 + 3 + ……. ...

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  20. Find the sum of all 11 term of an AP whose middle most term in 30.

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