Sequences & Series
Sequences and Series
Grade None
Question:
<p>32. 4n kk+1) Let the first term of a series be T, = 6 and its r term T, = 3T,_; + 6,,7 = 2, 3, _ n. Ifthe sum of [JEE (Advanced) 2013] Let S,=)°(-1) ? &’ . Then S;, can take value(s) ka the first n terms of this series is (0° -12n +39)(4.6" —5.3" +1). Then n is equal to</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 \(1\).
Correct Answer: 1