Sequences & Series
AP — Finding Σ₁₇aᵢ
nta_pyq_2026_jan
Grade 11
Question:
Consider an A.P.: $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and $\displaystyle\sum_{i=1}^n a_i=\dfrac{525}{2}$, then $\displaystyle\sum_{i=1}^{17}a_i$ is equal to
Step-by-Step Solution
Key Concept: $d=-3/4$. $a_n=a_1+(n-1)d=a_1/4\Rightarrow(n-1)\cdot(-3/4)=-3a_1/4\Rightarrow n-1=a_1$. $S_n=5n(n-1)/8=525/2\Rightarrow n(n-1)=420\Rightarrow n=21$, $a_1=20$.
$n=21$, $a_1=20$. $\sum_{i=1}^{17}a_i=238$.
Correct Answer: 3