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Prove that if a, b, c are in HP, if and ...

Prove that if a, b, c are in HP, if and only if `(a)/(c )=(a-b)/(b-c)`.

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FULL MARKS-BINOMIAL THEOREM, SEQUENCES AND SERIES -Additional Questions Solved
  1. Prove that if a, b, c are in HP, if and only if (a)/(c )=(a-b)/(b-c).

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  2. Find the coefficient of the term involving x^(32) and x^(-17) in the e...

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  3. Find a positive value of m for which the coefficient of x^(2) in the e...

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  4. In the binomial expansion of (1+a)^(m+n), prove that the coefficients ...

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  5. The coefficient of (r-1)^(th), r^(th), and (r+1)^(th) terms in the exp...

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  6. Find the value of (a^(2)+sqrt(a^(2)-1))^(4)+(a^(2)-sqrt(a^(2)-1))^(4)

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  7. Show that the coefficient of the middle term in the expansion of (1+x)...

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  8. If three consecutive coefficients in the expansion of (1+x)^(n) are in...

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  9. If the sum of the coefficients in the expansion of (x+y)^(n) is 4096. ...

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  10. Find the coefficient of (1)/(x^(17)) in the expansion of (x^(4)-(1)/(x...

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  11. If p is a real number and if the middle term in the expansion of ((p)/...

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  12. Find the first five terms of the sequence given by {{:(" " a(1...

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  13. Find the 18^(th) and 25^(th) terms of the sequence defined by a(n)=...

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  14. Write the first six terms of the sequences given by (i) a(1)=a(2)...

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  15. An A.P. consists of 21 terms. The sum of the three terms in the middle...

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  16. Prove that the product of the 2^(nd) and 3^(rd) terms of an arithmetic...

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  17. If the p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c respecti...

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  18. If a, b, c are in A.P. and p is the A.M. between a and b and q is the ...

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  19. If x, y, z be respectively the p^(th), q^(th) and r^(th) terms of a G....

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  20. If the ratio of the sums of m terms and n terms of an A.P. be m^(2) : ...

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  21. Determine the number of terms of geometric progression {a(n)} if a(1)=...

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