Sequences & Series
AP with given terms; mean of derived sequence
MJMT_Full_Test_05
Grade 12
Question:
Let $x_1, x_2, \ldots, x_{100}$ be an A.P. with $x_1=1$ and $x_{100}=199$. If $y_i=i(x_i+1)$; $i=1,2,\ldots,100$, then mean of $y_1, y_2, \ldots, y_{100}$ is
6867
6767
6967
none of these
Step-by-Step Solution
Key Concept: Common difference $d=2$, so $x_i=2i-1$. Then $y_i=i(2i)=2i^2$. Mean $=\frac{2}{100}\sum_{i=1}^{100}i^2$.
Mean $=6767$.
Correct Answer: 2