Home
Class 11
MATHS
Suppose four distinct positive numbersa(...

Suppose four distinct positive numbers`a_(1),a_(2),a_(3),a_(4)` are in GP. Let `b_(1)=a_(1),b_(2)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)" and " b_(4)=b_(3)+a_(4)`
Statement 1 The numbers`b_(1),b_(2),b_(3),b_(4)` are neither in AP nor in GP.
Statement 2 The numbers `b_(1),b_(2),b_(3),b_(4)` are in HP.

A

Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.

B

Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.

C

Statement -1 is true, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
Let r be the common ratio of the G.P.
We have,
`b_(1)=a_(1),b_(2)=a_(1)+a_(2)=a_(1)(1+r),b_(3)=b_(2)+a_(3)=a(1+r+r^(2))`,
`b_(4)=b_(3)+a_(4)=a_(1)(1+r+r^(2)+r^(3))`
Clearly, `b_(1),b_(2),b_(3),b_(4)` are neither in A.P. nor in G.P.
So, statement -1 is correct.
Also, `b_(1),b_(2),b_(3),b_(4)` are not in H.P. So, statement -2 is false.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|129 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|80 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1)+,a_(b)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If (a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) -a_(2))^(2) = (a_(1)-a_(4))^(2)

If a and b are distinct positive real numbers such that a, a_(1), a_(2), a_(3), a_(4), a_(5), b are in A.P. , a, b_(1), b_(2), b_(3), b_(4), b_(5), b are in G.P. and a, c_(1), c_(2), c_(3), c_(4), c_(5), b are in H.P., then the roots of a_(3)x^(2)+b_(3)x+c_(3)=0 are

If the points (a_(1),b_(1))m(a_(2),b_(2))" and " (a_(1)-a_(2),b_(2)-b_(2)) are collinear, then prove that a_(1)/a_(2)=b_(1)/b_(2)

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

The number of functions from f:{a_(1),a_(2),...,a_(10)} rarr {b_(1),b_(2),...,b_(5)} is

Let A = {a_(1), b_(1), c_(1)} and B = {a_(2), b_(2)} (i) A xx B (ii) B xx B

The determinant |(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2)),(b_(3)+c_(3),c_(3)+a_(3),a_(3)+b_(3))|