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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 AP.

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

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

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,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.

If a(1/b +1/c) , b (1/c +1/a),c(1/a +1/b) are in AP , prove tht a^(2)(b+c) ,b^(2) (c+a) , 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.

Show that (a^(2) +ab+b^(2)) ,(c^(2) +ac +a^(2)) and ( b^(2) +bc+ c^(2)) are in AP, if a,b,c are in AP.

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^(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 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.

AGRAWAL PUBLICATION-ARITHMETIC PROGRESSIONS-EXAMPLE
  1. Find the 16^(th)term of the AP,2,7,12,17,……

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  2. Find the mean of first eleven natural numbers.

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

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  4. If the 17^(th) term of an A.P exceeds its 10^(th) term by 7, Find the ...

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  5. Hoe many multiples of 4 die between 10 and 205?

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  6. Determine the A.P. whose third term is 16 and 7^(th) term exceeds the ...

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  7. Two AP's have the same common difference.The first term of one AP is 2...

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  8. Which term of the AP 3,15,27, 39,…. Will be 120 more than its 21st ter...

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  9. If Sn the sum of first n terms of an AP is given by Sn =3n^2-4n, find ...

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

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  11. If seven times the 7^(th) term of an A.P is equal to eleven times the ...

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

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

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  14. Determine the AP whose third term is 5 and the seventh term is 9.

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

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  16. Find the number of natural numbers between 102 and 998 whixh are divis...

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  17. For what value of n, are the n^(th) terms of two A.Ps 63,65,67… and 3,...

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

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  19. In an AP, if Sn + S7 =167 and S(10) =235, then find th AP, where Sn de...

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  20. The 4^(th) erm of an AP. Is zero. Prove that the 25th term of the A.P ...

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