MP Board · Class 11 · Mathematics · Sequences and SeriesWhich term of the G.P. 2, 4, 8, 16, ... is 512?
Step-by-Step Solution
Using the formula for the $n$th term of a G.P., $a_n = ar^{n-1}$. Here, $a = 2$, $r = 2$, and $a_n = 512$. So, $512 = 2 \times 2^{n-1}$, which means $256 = 2^{n-1}$. Since $256 = 2^8$, we have $2^{n-1} = 2^8$, giving $n - 1 = 8$, so $n = 9$. Therefore, the correct option is C.
Detailed Options Breakdown
Option : 7
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 1: 8
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 2: 9 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 10
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.