Suppose four distinct positive numbers `a_(1),a_(2),a_(3),a_(4)` are in G.P. Let `b_(1)=a_(1), b_(2)=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.

Options

A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true

Answer

C

Explanation

`b_(1)=a_(1),b_(2)=b_(1)+a_(2)=a_(1)+a_(2),b_(3)=b_(2)+a_(3)=+a_(1)+a_(2)+a_(3)`
and `b_(4)=b_(3)+a_(4)=a_(1)+a_(2)+a_(3)+a_(4)`
Hence, `b_(1),b_(2),b_(3),b_(4)` are neither in AP nor in GP and nor in HP.