Sequences & Series
Series Summation
Grade 11
Question:
<p>Let ay, a2, a3 a,, be real numbers satisfying 144 138 141 147 2 a, =15, 27 - 2a, > Oand ay, = 2a,_1- Ay_2 for k = 3,4. 11. 29. The sum of the series +... up to 10 terms is -31+1' * 1-327 +2" * 1-3:3°+3* If ata; +a, =90, then the value of a,+a, 11 11 a1 ig equal to [IIT JEE 2010] [JEE (Main) 2024]</p>
Step-by-Step Solution
Key Concept: Look for the progression structure before computing. The right formula usually appears only after the sequence is rewritten cleanly.
Notice that the important step is to identify which progression formula is actually relevant here. A clever move here is to rewrite the given information into a standard form before computing. Now, we invoke the power of the appropriate sequence identity, simplify carefully, and confirm the answer as $C$.
Correct Answer: 3