MP Board · Class 11 · Mathematics · Sequences and SeriesIf the sum of $n$ terms of a series is $Sn = 2^n - 1$, what type of sequence does it represent?
Step-by-Step Solution
Let's find the first few terms. $a_1 = S_1 = 2^1 - 1 = 1$. $S_2 = 2^2 - 1 = 3$, so $a_2 = S_2 - S_1 = 3 - 1 = 2$. $S_3 = 2^3 - 1 = 7$, so $a_3 = S_3 - S_2 = 7 - 3 = 4$. The sequence is 1, 2, 4, 8, ... which is a Geometric Progression with $a=1$ and $r=2$. Therefore, the correct option is B.
Detailed Options Breakdown
Option : Arithmetic Progression
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 1: Geometric Progression (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: Harmonic Progression
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 3: None of these
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.