NCERT · Class 10 · Mathematics · Arithmetic ProgressionsWhat is the sum of the first 10 terms of the AP: 2, 7, 12, ...?
Step-by-Step Solution
The sum of $n$ terms is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$. Here, $a = 2$, $d = 5$, and $n = 10$. Thus, $S_{10} = \frac{10}{2}[2(2) + (10 - 1)5] = 5[4 + 9(5)] = 5[4 + 45] = 5(49) = 245$. Therefore, option B is correct.
Detailed Options Breakdown
Option : 225
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 1: 245 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 250
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 3: 255
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
💡 Study Guide: This question tests core syllabus concepts from Arithmetic Progressions. For formulas, key summaries, and mock exam reference guides, read the full Arithmetic Progressions Revision Notes.