Home
Class 12
MATHS
If a(1) , a(2), "……………" a(n) are in H.P....

If `a_(1) , a_(2), "……………" a_(n)` are in H.P., then the expression `a_(1) a_(2) + a_(2) a_(3)+"…….."+ a_(n-1) a_(n)` is equal to `:`

A

`n(a_(1) - a_(n))`

B

`(n-1) ( a_(1) - a_(n))`

C

`na_(1) a_(n)`

D

`(n-1) a_(1) a_(n)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise LATEST QUESTIONS|11 Videos
  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos
  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos
  • RELATIONS

    MODERN PUBLICATION|Exercise RCQS|6 Videos
  • SETS

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|6 Videos

Similar Questions

Explore conceptually related problems

If a_(1) , a_(2) , a_(3),"………."a_(n) are in H.P. , then a_(1), a_(2) + a_(2) a_(3) + "………" + a_(n-1)a_(n) will be equal to :

If 1, a_(1), a_(2). ..., a_(n-1) are n roots of unity, then the value of (1 - a_(1)) (1 - a_(2)) .... (1 - a_(n-1)) is :

If a_(1),a_(2) , a_(3),"……..",a_(n) are in H.P. , then : (a_(1))/( a_(2) + a_(3) +"........."+a_(n)),(a_(2))/(a_(1) + a_(3)+"..........."+a_(n)),"......",(a_(n))/(a_(1)+a_(2)+"........"a_(n-1)) are in :

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(r ) gt 0, r in N and a_(1), a_(2) , a_(3) ,"……..",a_(2n) are in A.P. then : (a_(1) + a_(2n))/( sqrt( a_(1))+ sqrt(a_(2))) + ( a_(2) + a_(2n-1))/(sqrt(a_(2)) + sqrt(a_(3)))+"......"(a_(n)+a_(n+1))/(sqrt(a_(n))+sqrt(a_(n+1))) is equal to :

If a_(1)a_(2)a_(3)…….a_(9) are in A.P. then the value of |(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9))| is

If a_(1) , a_(2),"………",a_(n) are n non-zero real numbers such that ( a_(1)^(2) +a_(2)^(2) + "........."+a_(n-1)^(2) ) ( a_(2)^(2) + a_(3)^(2) + "........"+a_(n)^(2))le(a_(1) a_(2) + a_(2) a_(3) +".........." +a_(n-1) a_(n))^(2), a_(1), a_(2),".........",a_(n) are in :

if a_(1), a_(2) , a_(3),"……",a_(n) are in A.P. with common difference d, then the sum of the series : sin d [coseca_(1) coseca_(2) + cosec a_(2) cosec a_(3) + "…."cosec a_(n-1) cosec a_(n)] is :

If a_(1), a_(2), a_(3)"….." are in G.P. , then the value of Delta= |{:(log a_(n),loga_(n+1),loga_(n+2)),(log a_(n+3),loga_(n+4),loga_(n+5)),(loga_(n+6),loga_(n+7),loga_(n+8)):}| is :

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. The first term of a G. P. is 1. The sum of the third and fifth terms i...

    Text Solution

    |

  2. Suppose a,b,c are in A.P. and a^(2) , b^(2) , c^(2) are in G.P. If a ...

    Text Solution

    |

  3. If sum of the roots of the quadratic equation ax^(2) + bx+c = 0 is equ...

    Text Solution

    |

  4. If f(x) is a polynomial function of second degree. IF f(1) = f(-1) and...

    Text Solution

    |

  5. The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4...

    Text Solution

    |

  6. If s= sum(n=0)^(oo) a^(n) , y = sum(n=0)^(oo) b^(n) , z= sum (n=0)^(oo...

    Text Solution

    |

  7. If alpha, beta are roots of ax^(2) + bx + c =0 , a cancel(=) 0 and alp...

    Text Solution

    |

  8. Let a(1) , a(2) , a(3) , "……………" be terms of an A.P. If (a(1) + a(2) +...

    Text Solution

    |

  9. If a(r ) gt 0, r in N and a(1), a(2) , a(3) ,"……..",a(2n) are in A.P....

    Text Solution

    |

  10. Let x,y,z be three positive prime numbers. The progression in which sq...

    Text Solution

    |

  11. If x = sum(n=0)^(oo) a^(n) .,y=sum(n=0)^(oo) b^(n) , z = sum(n=0)^(oo)...

    Text Solution

    |

  12. underset("n-digits")((666"……"6))^(2) +underset("n-digits") (( 888"…" 8...

    Text Solution

    |

  13. If sum(r=1)^(n) t(r ) = sum(k=1)^(n) sum(j=1)^(k) sum(i=1)^(j) 2, then...

    Text Solution

    |

  14. The odd numbers are divides as follows : {:(,,1,3,,),(,5,7,9,11,),(1...

    Text Solution

    |

  15. If x(1), x(2), x(3) as well as y(1) , y (2) , y (3) are in G.P. with t...

    Text Solution

    |

  16. If a(1) , a(2), "……………" a(n) are in H.P., then the expression a(1) a(2...

    Text Solution

    |

  17. In a geometric progression consisting of positive terms, each term equ...

    Text Solution

    |

  18. The first two terms of a geometric progression add upto 12. The sum of...

    Text Solution

    |

  19. The sum to infinity of the series : 1+ ( 2)/( 3) + ( 6)/( 3^(2)) +(...

    Text Solution

    |

  20. If the sum of first n terms of an A.P. is cn^(2) , then the sum of squ...

    Text Solution

    |