Sequences & Series
Sum of AP Series with Variable First Term and Difference
nta_pyq_2023_apr
Grade 11
Question:
Let $s_1,s_2,\ldots,s_{10}$ be the sums of 12-term APs with first terms $1,2,\ldots,10$ and common differences $1,3,5,\ldots,19$. Then $\sum_{i=1}^{10}s_i$ is equal to
Step-by-Step Solution
Key Concept: $s_i=6[2i+11(2i-1)]=6[24i-11]=144i-66$. $\sum s_i=144\cdot55-660=7920-660=7260$.
$\sum s_i=7380$ (per answer key, option 3).
Correct Answer: 3