Question

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 and b_4=b_3+a_1.`
A. Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I
B. Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I
C. Statement I is true, Statement II is false
D. Statement I is false, Statement II is true

Answer 1

Correct Answer - C
Let `a_(1) = 1, a_(2) = 2, rArr a_(3) = 4, a_(4) = 8`
`:. B_(1) = 1, b_(2) =3, b_(3) = 7, b_(4) = 15`
Clearly, `b_(1), b_(2), b_(3), b_(4)` are not in HP.
Hence, Statement II is false
Statement I is already true