CBSE · Class 10 · Mathematics · Arithmetic ProgressionsWhat is the sum of the first 22 terms of the AP: 8, 3, -2, ...?
Step-by-Step Solution
Here, $a = 8$, $d = 3 - 8 = -5$, and $n = 22$. Using $S_n = \frac{n}{2}[2a + (n - 1)d]$, we get $S_{22} = \frac{22}{2}[2(8) + (22 - 1)(-5)] = 11[16 + 21(-5)] = 11[16 - 105] = 11(-89) = -979$. Therefore, option A is correct.
Detailed Options Breakdown
Option : -979 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: -961
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 2: -989
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 3: -970
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.