NCERT · Class 11 · Mathematics · Sequences and SeriesIf $a, b, c$ are in A.P., then which of the following relations is always true?
Step-by-Step Solution
By definition of an arithmetic progression, the difference between consecutive terms is constant, i.e., $b - a = c - b$. Rearranging this equation gives $2b = a + c$, or $b = \frac{a + c}{2}$. Therefore, the correct option is A.
Detailed Options Breakdown
Option : $2b = a + c$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $b^2 = ac$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 2: $b = a + c$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 3: $b = \sqrt{ac}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
💡 Study Guide: This question tests core syllabus concepts from Sequences and Series. For formulas, key summaries, and mock exam reference guides, read the full Sequences and Series Revision Notes.