Home
Class 12
MATHS
If a ,a1, a2, a3, a(2n),b are in A.P. a...

If `a ,a_1, a_2, a_3, a_(2n),b` are in A.P. and `a ,g_1,g_2,g_3, ,g_(2n),b` . are in G.P. and `h` s the H.M. of `aa n db ,` then prove that `(a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h`

A

`(2n)/(h)`

B

2nh

C

nh

D

`(n)/(h)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos
  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise For Session 7|7 Videos
  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise For Session 4|10 Videos
  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos
  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1, a_2,a_3,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.P.

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)

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)) .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a_1, a_2 , ............, a_n are in A.P. and a_i >0 for all i , prove that : 1/(sqrt a_1+sqrt a_2)+1/(sqrt a_2+sqrt a_3)+.............+ 1/(sqrt (a_(n-1))+sqrt a_n)= (n-1)/(sqrt a_1+sqrt a_n) .

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common ratio r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

if a_(1),a_(2),…….a_(n),……. form a G.P. and a_(1) gt 0 , for all I ge 1 |{:(log a_(n),,loga_(n+1),,log a_(n+2)),(log a_(n+3),,log a_(n+4),,log a_(n+5)),(log a_(n+6),,loga_(n+7),,log a_(n+8)):}|