Sequences & Series
AP — S₁₅−S₅ Given S₂₀ and S₁₀
nta_pyq_2024_jan
Grade 11
Question:
Let $S_a$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-S_5$ is:
Step-by-Step Solution
Key Concept: $S_{20}=10(2a+19d)=790\Rightarrow2a+19d=79$. $S_{10}=5(2a+9d)=145\Rightarrow2a+9d=29$. Solve: $d=5,a=-8$. Then compute $S_{15}-S_5$.
$a=-8,d=5$. $S_{15}-S_5=405-10=395$.
Correct Answer: 1