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 $b _{4}= b _{3}+ a _{4}$
STATEMENT-1: The numbers $b _{1}, b _{2}, b _{3}, b _{4}$ are neither in $A.P$. nor in $G.P$.
and
STATEMENT-2 : The numbers $b _{1}, b _{2}, b _{3}, b _{4}$ are in $H.P$.

• 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 1

Answer: (C)

$b _{1}= a _{1}, b _{2}= a _{1}+ a _{2}, b _{3}= a _{1}+ a _{2}+ a _{3}, b _{4}= a _{1}+ a _{2}+ a _{3}+ a _{4}$
Hence $b _{1}, b _{2}, b _{3}, b _{4}$ are neither in $A.P. $ nor in $G.P$. nor in $H.P$.