Home
Class 11
MATHS
If first and (2n-1)^th terms of an AP, ...

If first and `(2n-1)^th` terms of an AP, GP. and HP. are equal and their nth terms are a, b, c respectively, then (a) a=b=c (b)a+c=b (c) a>b>c and `ac-b^2=0` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If first and (2n-1)^th terms of an AP, GP. and HP. are equal and their nth terms are a, b, c respectively, then (a) a=b=c (b)a+c=b (c) a>b>c (d) none of these

If the first and (2n-1)^(th) terms of an A.P, a G.P and an H.P of positive terms are equal and their (n+1)^(th) terms are a, b & c respectively then

If a ,\ b ,\ c are in proportion, then (a) a^2=b c (b) b^2=a c (c) c^2=a b (d) None of these

If a ,b ,c ,d in R^+ and a ,b ,c,d are in H.P., then (a) a+d > b+c (b) a+b > c+d (c) a+c > b+d (d)none of these

If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c

If the first, second and last term of an A.P. are a ,\ b and 2a respectively, its sum is (a b)/(2(b-a)) (b) (a b)/(b-a) (c) (3a b)/(2(b-a)) (d) none of these

If a,b,c in G.P. x,y be the A.M.\'s between a,b and b,c respectively then (a/x+c/y)(b/x+b/y)= (A) 2 (B) -4 (C) 4 (D) none of these

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are both a ,\ b\ a n d\ c respectively show that a^(b-c)b^(c-a)c^(a-b)=1.

If first term of a GP is a, third term is b and (n+1)th term is c. The (2n+1)th term of a GP is

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a , b ,c are three distinct positive real numbers in G.P., then pro...

    Text Solution

    |

  2. For xgeq0 , the smallest value of the function f(x)=(4x^2+8x+13)/(6(1...

    Text Solution

    |

  3. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

    Text Solution

    |

  4. For positive real numbers a ,bc such that a+b+c=p , which one holds?...

    Text Solution

    |

  5. If x ,y ,z are positive numbers is AdotPdot,t h e n (a)y^2geqx z ...

    Text Solution

    |

  6. int 1/((1-x^2)sqrt(1+x^2))dx

    Text Solution

    |

  7. If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...

    Text Solution

    |

  8. The minimum value of |2z-1|+|3z-2| is

    Text Solution

    |

  9. If a ,b ,c ,d in R^+ such that a+b+c=18 , then the maximum value of a...

    Text Solution

    |

  10. If x ,y and z are posirive real umbers and x=(12-y z)/(y+z) . The max...

    Text Solution

    |

  11. Let x^2-3x+p=0 has two positive roots aa n db , then minimum value if ...

    Text Solution

    |

  12. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+...

    Text Solution

    |

  13. If a ,b ,c ,d in R^+and a ,b ,c,d are in H.P., then (a)a+d > b+c (...

    Text Solution

    |

  14. The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3...

    Text Solution

    |

  15. If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-...

    Text Solution

    |

  16. If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(10...

    Text Solution

    |

  17. For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is a(-oo,-...

    Text Solution

    |

  18. If a ,b ,c are the sides of a triangle, then the minimum value of a/(...

    Text Solution

    |

  19. If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)d a+(log)b ...

    Text Solution

    |

  20. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alw...

    Text Solution

    |