Question:

Let $x_1,x_2,\ldots,x_{100}$ be in AP, $x_1=2$, mean $=200$. If $y_i=i(x_i-i)$, then mean of $y_1,\ldots,y_{100}$ is

10100

10101.50

10049.50

10051.50

Step-by-Step Solution

Key Concept: $d=4$ (from $\sum x_i=20000$). $x_i=4i-2$. $y_i=i(3i-2)=3i^2-2i$. Mean $=\frac{1}{100}\sum_{i=1}^{100}(3i^2-2i)$.

Mean $=10049.50$.

Correct Answer: 3