Sequences & Series
Arithmetic Progression
Grade 11
Question:
<p>If <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> are four unequal positive numbers which are in A.P., then</p>
<p>(A) [Option text not provided]</p>
<p>(B) [Option text not provided]</p>
<p>(C) <i>ad</i> < <i>bc</i></p>
<p>(D) [Option text not provided]</p>
Step-by-Step Solution
Key Concept: For numbers in A.P., the product of extremes is less than the product of means when all terms are positive and unequal.
<p>For four unequal positive numbers in A.P., if we denote them as \(a, a+d, a+2d, a+3d\) where \(d > 0\), then \(ad = a(a+3d) = a^2 + 3ad\) and \(bc = (a+d)(a+2d) = a^2 + 3ad + 2d^2\). Since \(2d^2 > 0\), we have \(ad < bc\).</p>
Correct Answer: C