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If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show that the sum of (p + q) terms is `(p+q)/2[(a + b) + (a- b)/(p - q)]` .

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. In an A.P., S(3)=6 and S(6)=3 prove that: 2(2n+1)S(n+4)=(n+4)S(2n+1)...

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  2. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

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  3. If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show...

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  4. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

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  5. Find the A.M. between : 3.7 and 5.5.

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  6. Find the A.M. between : 6 and -8.

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  7. Insert 3 arithmetic means between : 3 and 15.

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  8. Insert 3 arithmetic means between : 5 and 21.

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  9. Insert 5 arithmetic means between 8 and 26.

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  10. Insert 6 arithmetic means between 3 and 24.

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  11. Insert 10 arithmetic means between 2 and 57.

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  12. If A is the A.M. between a and b, prove that : (A-a)^(2) +(A-b)^(2)=...

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  13. If A is the A.M. between a and b, prove that : 4(a-A)(A-b)=(a-b)^(2...

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  14. If A1 and A2 are two A.M.’s between a and b, prove that : (2A1-A2)(2...

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  15. If A1 and A2 are two A.M.’s between a and b, prove that : A1+A2 =a+b...

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  16. Insert 10 A.M.’s between 5 and -17 and prove that their sum is ten tim...

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  17. n arithmetic means are inserted between 3 and 17 such that ratio of fi...

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

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  19. 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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  20. Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the ge...

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