Sequences & Series
Arithmetic Progression (AP)
Grade 11
Question:
<p>Apack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from 33. Let the positive integers be written in the form: the pack and the sum of the numbers on the remaining cards is 1224. If the smaller to the numbers 1 on the removed cards is k, then k - 20 = [JEE (Advanced) 2013] 2 3</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 \(6\).
Correct Answer: 6