Sequences & Series
Arithmetic Progression (AP)
Grade 11
Question:
<p>Let an, n € N is an A.P. with common difference 'd' and all whose terms are non-zero. If n 12. If x € R, the numbers (5 +5"), am (2 5 +25") form an A.P. then ‘a’ must lie in the interval approaches infinity, then the sum + will approach</p>
<p>[5]</p>
<p>[2, 5] (©) [5, 12]</p>
<p>[12, «) a a, a,a, net</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 $B$.
Correct Answer: 2