Sequences & Series
Recurrence Relation — Sum of Series
nta_pyq_2024_apr
Grade None
Question:
Let the first term of a series be $T_1=6$ and its $r$th term $T_r=3T_{r-1}+6^r$, $r=2,3,\ldots,n$. If the sum of the first $n$ terms of this series is $\dfrac{1}{5}(n^2-12n+39)(4\cdot6^n-5\cdot3^n+1)$, then $n$ is equal to
Step-by-Step Solution
Key Concept: Solve the recurrence $T_r=3T_{r-1}+6^r$ and sum to get $S_n$. Match with the given formula to determine $n$.
$n=6$.
Correct Answer: 6