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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.

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EDUCART PUBLICATION-ARITHMETIC PROGRESSIONS-SHORT ANSWER (SA - I) TYPE QUESTIONS
  1. Show that (a-b)^2,\ (a^2+b^2) and (a+b)^2 are in A.P.

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  2. The 17^(t h) term of an AP exceeds its 10^(t h) term by 7. Find the co...

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  3. How many multiples of 4 lie between 10 and 250?

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  4. Determine the AP whose third term is 16 and the 7th term exceeds the 5...

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  5. Two A.P have the same common difference. The first term of one A.P is ...

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  6. Which term of the AP 3, 15, 27, 39,… will be 120 more than its 21st te...

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  7. If S(n) the sum of first n terms of an A.P. is given by Sn = 3n^(2) ...

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  8. Find the sum of first 10 multiples of 3,

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  9. If seven times the 7th term of an AP is equal to eleven times the 11th...

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  10. The 10^(th) term of an A.P. is -4 and its 22^(nd) term is (-16). Find ...

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  11. Find how many integers between 200 and 500 are divisible by 8.

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  12. Determine the AP whose 3^(r d)term is 5 and the 7^(t h)term is 9.

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  13. If the sum of the first 9 terms of an AP is equal to the sum of its fi...

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  14. Find the number of natural numbers between 102 and 998 which are divis...

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  15. For what value of n, the nth terms of the arithmetic progressions 63, ...

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  16. The common difference between the terms of two AP's is same. If the di...

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  17. In an AP, it is given that S(5) + S(7) = 167 "and" S(10) = 235, then f...

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  18. If the 4th term of an A.P. is zero, prove that the 25th term of the A....

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  19. For an AP, it is given that first term (a)= 5 and Common Difference (d...

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  20. If 6 times the 6^(th) term of an A.P, is equal to 9 times the 9^(th) t...

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