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If a, b, c are in AP, then prove that `(a-c)^2 =4(b^2 -ac)`

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If a,b,c are in A.P.then prove that: (a-c)^(2)=4(b^(2)-ac)a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2))

if a,b,c are in AP, prove that (a-c)^(2) = 4( b^(2) -ac)

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

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

If a,b,c are in A.P.,prove that: (a-c)^(2)=4(a-b)(b-c)a^(2)+c^(2)+4ac=2(ab+bc+ca)a^(3)+c^(3)+6abc=8b^(3)

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

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

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

MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. Each term of an A.P. is doubled,. Is the resulting sequence also an A....

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  2. If the mth term of an A.P. be 1//n and nth term be 1//m then show that...

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  3. If a, b, c are in AP, then prove that (a-c)^2 =4(b^2 -ac)

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  4. Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P...

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  5. How many numbers of two digits are divisible by 7?

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  6. Let S(n) denotes the sum to terms of an A.P. whose first term is a . I...

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  7. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  8. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  9. IF the sum of p terms of an AP is q and the sum of q terms is ...

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  10. In a G.P. the first term is a, second term is b and the last term is ...

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  11. Find the sum of all natural numbers between 1 and 100, which are divis...

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  12. A man gets an appointment with two options. Either he can accept Rs. 4...

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  13. A fanner buys a used tractor for Rs 12000. He pays Rs 6000 cash and...

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  14. Shamshad Ali buys a scooter for Rs. 2200. He pays Rs. 4000 cash and ...

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  15. Two cars start together in the same direction from the same place. The...

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  16. The ages of the students of a class form an A.P. whose common differen...

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  17. "If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a...

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

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  19. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  20. If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

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