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Show that `(a-b)^2,\ (a^2+b^2)` and `(a+b)^2` are in A.P.

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If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 are in A.P.

If a, b, c are in A.P., show that: (b + c), (c + a) and (a + b) are also in A.P.

If a,b and c are in A.P, show that (b+c), (c+a) and (a+b) are also in A.P.

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a^(2), b^(2),c^(2) are in A.P prove that (a)/(b+c), (b)/(c+a) ,(c)/(a+b) are in A.P.

If (b+c)^(-1), (c+a)^(-1), (a+b)^(-1) are in A.P. then show that (a)/(b+c) , (b)/(c+a) , (c)/(a+b) are also in A.P.

If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. Find the value of x for which (8x+4),\ (6x-2) and (2x+7) are in A.P...

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  2. If x+1,\ 3x and 4x+2 are in A.P., find the value of x .

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  3. Show that (a-b)^2,\ (a^2+b^2) and (a+b)^2 are in A.P.

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  4. Find the sum of 20 terms of the AP 1, 4, 7, 10,....

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  5. Find the sum of first n natural numbers.

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  6. Find the sum of all odd integers between 2 and 100 divisible by 3

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  7. How many terms of the series 54,51, 48,.. be taken so that their sum i...

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  8. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  9. The sum of n, 2n, 3n terms of an A.P. are S1, S2, S3 respectively. Pro...

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  10. The sums of n terms of three arithmetical progressions are S1, S2and ...

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  11. If the sum of first m terms of an A.P. is the same as the sum of its f...

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  12. The ratio of the sums of m and n terms of an A.P. is m^2: n^2 .Sho...

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  13. A manufacturer of TV sets produced 600 sets in the third year and 700 ...

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  14. A contract on construction job specifies a penalty for delay of com...

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  15. A sum of Rs 280 is to be used to award four prizes. If each prize a...

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  16. In a school students thought of planting trees in and around the sc...

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  17. 200 logs are stacked in the following manner: 20 logs in the bottom ...

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  18. The digits of a positive integer, having three digits, are in A.P. and...

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  19. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

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  20. The houses of a row are numbered consecutively from 1 to 49. Show that...

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