Home
Class 12
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

A

`a+c =2b`

B

`a ge b ge c`

C

`(2ac)/(a +c) =b`

D

` a c = b ^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • SOLUTION OF TRIANGLES

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|12 Videos

Similar Questions

Explore conceptually related problems

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

The 4th, 7th and 10 th terms of a GP are a, b, c, respectively. Prove that b^(2)=ac .

The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that b^(2)=ac .

If the 4 th,7 th and 10 th terms of a GP are a,b and c respectively,then the reason between a, b and c is

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

If a, b, c are in HP, then (a - b)/( b- c) is equal to

If p^(th),q^(th) and r^(th) terms of an A.P and G.P are both a,b and c respectively then show that a^(b-c).b^(c-a).c^(a-b)=1

VIKAS GUPTA (BLACK BOOK)-SEQUENCE AND SERIES -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

    Text Solution

    |

  2. If a, b, c are distinct positive real numbers such that the quadratic ...

    Text Solution

    |

  3. If a,b,c are in H.P, where a gt c gt 0, then :

    Text Solution

    |

  4. In an A.P. let T(r) denote r ^(th) term from beginning, T(p) - (1)/(q ...

    Text Solution

    |

  5. Which of the following statement (s) is (are) correct ?

    Text Solution

    |

  6. If a,b,c are in 3 distinct numbers in H.P. a,b,c gt 0, then :

    Text Solution

    |

  7. All roots of equation x ^(5) -40 x ^(4) + alphax ^(3) + beta x ^(2) + ...

    Text Solution

    |

  8. Let a (1), a(2), a(3)……. be a sequence of non-zero rela numbers with a...

    Text Solution

    |

  9. Given a,b,c are in A.P. b,c,d are in G.P. and c,d,e are in H.P. if a =...

    Text Solution

    |

  10. The number a, b, c in that order form a term A.P and a + b + c = 60. T...

    Text Solution

    |

  11. If (x ^(2) +x+1) + (x^(2) + 2x +3) + (x^(2) + 3x +5) + ….. + (x ^(2) +...

    Text Solution

    |

  12. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

    Text Solution

    |

  13. Let x,y,z in (0, (pi)/(2)) are first three consecutive terms of an ari...

    Text Solution

    |

  14. If the number 16, 20, 16, d form a A.G.P. then d can be equal to :

    Text Solution

    |

  15. If S(r) = sqrt(r+ sqrt(r+sqrt(r+sqrt(......oo)))) , r gt 0 then which...

    Text Solution

    |

  16. Consider the A.P. 50,48,46,44 ……. If S (n) denotes the sum to n term...

    Text Solution

    |

  17. Let S(n)be the sum to n terms of the series (2)/(1 ^(2)) + (5)/(1 ^(2)...

    Text Solution

    |

  18. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

    Text Solution

    |