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Show that (a-b)^2,\ (a^2+b^2) and (a+b)^...

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

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Show that (a - b)^(2), (a^(2) + b^(2)) " and " (a + b)^(2) are in AP.

If a,b,c are in AP, show that (i) (b+c) , (c+a) and (a +b) are in AP. (ii) a^(2) (b+c) , b^(2) (c +a) and c^(2) ( a+b) are in AP.

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

If a^(2),b^(2),c^(2) are in A.P.then show that: bc-a^(2),ca-b^(2),ab-c^(2) are in A.P.

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

If the angles A,B,C of /_\ABC are in A.P., and its sides a, b, c are in Gp., show that a^(2) , b^(2), c^(2) are in A.P.

If a,b,c are in Ap, show that (i) (b +c-a),(c+a-b) ,(a+b-c) are in AP. (bc -a^(2)) , (ca - b^(2)), (ab -c^(2)) are in AP.

Show that the sequence (a+b)^(2)(a^(2)+b^(2)),(a-b)^(2),... is an A.P.

If (b-c)^(2),(c-a)^(2),(a-b)^(2) are in A.P.then show that (1)/(b-c),(1)/(c-a),(1)/(a-b) are in A.P.

RD SHARMA-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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