Sequences & Series
Alternating series of squared terms
nta_pyq_2023_jan
Grade 11
Question:
The sum $1^2 - 2 \cdot 3^2 + 3 \cdot 5^2 - 4 \cdot 7^2 + 5 \cdot 9^2 - \ldots + 15 \cdot 29^2$ is ______.
Step-by-Step Solution
Key Concept: Group consecutive pairs: $(2k-1)(4k-3)^2 - 2k(4k-1)^2$ for $k = 1$ to 7, then add the last term $15 \cdot 29^2$. Alternatively find the pattern by computing pair sums.
The sum evaluates to 6952.
Correct Answer: 6952