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If a^2(b+c),b^2(c+a),c^2(a+b), are in A....

If `a^2(b+c),b^2(c+a),c^2(a+b),` are in A.P. show that either `a ,b ,c` are in A.P., or `a b+b c+c a=0.`

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. Prove that the sum of n arithmetic means between two numbers in n ti...

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

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  3. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  4. If n arithemetic means are inserted between 20 and 80 such that the ra...

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  5. Along a road lie an odd number of stones placed at intervals of 10 met...

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  6. A carpenter was hired to build 192 window frames. The first day he mad...

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  7. In a potato race 20 potatoes are placed in a line at intervals of 4m e...

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  8. We know that the sum of the interior angles of a triangle is180^0 . S...

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  9. If S1 be the sum of (2n+1) term of an A.P. and S2 be the sum of its od...

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  10. Divide 32 into four parts which are in A.P. such that the product of ...

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  11. If theta1,theta2,theta3, ,thetan are in AP, whose common difference ...

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  12. If (m+1) term of an A.P. is twice the(n+1) th term, prove that (3m+1) ...

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  13. If a1,a2,a3, ,an are in A.P. with common difference d(w h e r ed!=0), ...

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  14. If an A.P. is such that (a4)/(a7)=2/7, find (a6)/(a8) .

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  15. The 4th term of an A.P. is three times the first and the 7th term e...

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  16. Find the number of terms common to the two AP's 3,7,11,15.... 407 and...

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  17. the sum of terms equidistant from the beginning and end in an A...

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  18. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1a2)+...

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  19. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/...

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  20. The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that t...

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