NCERT · Class 10 · Mathematics · Arithmetic ProgressionsIf the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
Step-by-Step Solution
Given $a_2 = a + d = 13$ and $a_5 = a + 4d = 25$. Subtracting the first equation from the second gives $3d = 12 \implies d = 4$. Substituting $d = 4$ into $a + d = 13$ gives $a = 9$. Then, $a_7 = a + 6d = 9 + 6(4) = 9 + 24 = 33$. Hence, option A is correct.
Detailed Options Breakdown
Option : 33 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: 30
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 2: 37
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Arithmetic Progressions.
Option 3: 38
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.