CBSE · Class 11 · Mathematics · Sequences and SeriesFind the sum of the first 20 terms of the arithmetic progression 1, 3, 5, 7, ...
Step-by-Step Solution
The sum of the first $n$ terms of an A.P. is given by $S_n = \frac{n}{2}[2a + (n-1)d]$. Here, $a = 1$, $d = 2$, and $n = 20$. So, $S_{20} = \frac{20}{2}[2(1) + (20-1) \times 2] = 10[2 + 19 \times 2] = 10[2 + 38] = 10 \times 40 = 400$. Thus, the correct option is C.
Detailed Options Breakdown
Option : 200
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 1: 300
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 2: 400 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 420
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.