Sequences & Series
Arithmetic Progression (AP)
Grade 11
Question:
<p>the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is [JEE (Advanced) 2015] be</p>
Step-by-Step Solution
Key Concept: Express everything in terms of first term and common difference. That converts a vague-looking progression problem into plain algebra.
Notice that this question is really about the first term and common difference. A clever move here is to parameterize the progression using those two quantities and translate every condition into algebra. Now, we invoke the power of the standard A.P. term and sum formulas, simplify step by step, and confirm the answer as $103$.
Correct Answer: 103