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If the sequence `a_1, a_2, a_3,....... a_n ,dot` forms an A.P., then prove that `a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Prove that a sequence in an A.P., if the sum of its n terms is of the ...

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  2. The product of the three numbers in G.P. is 125 and sum of their pr...

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  3. If the sequence a1, a2, a3,....... an ,dot forms an A.P., then prove ...

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  4. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the g...

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  5. Three non-zero numbers a ,b , c are in A.P. Increasing a by 1 or incre...

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  6. A G.P. consists of an even number of terms. If the sum of all the t...

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  7. If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a ...

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  8. If the sum of n terms of a G.P. is 3-(3^(n+1))/(4^(2n)) , then find ...

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  9. Which term of the G.P. 2,1, 1/2,1/4, i s1/(128)?

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  10. 'n' A.M's are inserted between a and 2b, and then between 2a and b. If...

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  11. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find ...

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  12. The first and second terms of a G.P. are x^(-4) and x^n , respectively...

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  13. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0), then show t...

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  14. If n arithmetic means are inserted between 2 and 38, then the sum of t...

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  15. The first terms of  a G.P. is 1. The sum of the third and fifth ter...

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  16. If a ,b ,c ,d ,e ,f are A.M.s between 2 and 12, then find the sum a+b+...

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  17. Three positive numbers from an increasing G.P. If the middle term in t...

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  18. Divide 28 into four parts in an A.P. so that the ratio of the product ...

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

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  20. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

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