Sequences & Series
Sum of Series with Second-Order Differences
nta_pyq_2023_apr
Grade 11
Question:
If $S_n=4+11+21+34+50+\ldots$ to $n$ terms, then $\dfrac{1}{60}(S_{29}-S_9)$ is equal to
Step-by-Step Solution
Key Concept: $T_n=\frac{n(3n+5)}{2}$. $S_n=\frac{1}{2}(\frac{3n(n+1)(2n+1)}{6}+\frac{5n(n+1)}{2})$.
$\frac{S_{29}-S_9}{60}=223$.
Correct Answer: 1