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Suppose that a, b, c are in A.P. Prove t...

Suppose that a, b, c are in A.P. Prove that `a^2(b+c),b^2(c+a),c^2(a+b)` are in A.P.

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A N EXCEL PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. Insert 6 arithmetic means between 3 and 24.

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  2. Suppose that a, b, c are in A.P. Prove that 2b = a + c

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  3. Suppose that a, b, c are in A.P. Prove that a^2(b+c),b^2(c+a),c^2(a+b)...

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  4. If a, b, c are in A.P, prove that 1/(bc),1/(ca),1/(ab) are also in A.P...

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  5. Suppose a, b, c are in A.P. Prove that (ab+bc+ca)/(bc),(ab+bc+ca)/(ca)...

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  6. Suppose a, b, c are in A.P.Prove that a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)...

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  7. Suppose a^2,b^2,c^2 are in A.P. Prove that 2b^2=a^2+c^2

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  8. Suppose a^2,b^2,c^2 are in A.P. Prove that a/(b+c),b/(c+a),c/(a+b)are ...

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  9. Suppose (b+c)/a,(c+a)/b,(a+b)/c are in A.P.Prove 1/a,1/b,1/c are also ...

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  10. Suppose (b+c)/a,(c+a)/b,(a+b)/c are in A.P.Prove 1/a,1/b,1/c are also ...

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  11. Suppose a, b, c are in A.P. Prove that bc-a^2+ab-c^2=2b^2-(a^2+c^2). H...

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  12. Suppose a, b, c are in A.P. Prove that (a+2b-c)(2b+c-a)(c+a-b)=4abc

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  13. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

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  14. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

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  15. Find the 10^(th) term of the G.P. -3/4,1/2,-1/3,2/9,….

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  16. Which term of the progression 18, -12, 8,… is (512)/(729)?

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  17. The fourth, seventh and the last term of a G.P. are 10,80 and 2560 res...

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  18. The first term of a G.P is 1. The sum of the third and fifth terms is ...

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  19. Find sum of 5 + 55 + 555 + ... to n terms.

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  20. If x=1 +a + a^2+…. to oo, where |a| lt1 and y=1+b+b^2+… to oo , where ...

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