JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 28

Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\dfrac12$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. If $\bar x$ is the mean of new data, then the greatest integer less than or equal to $\bar x$ is ______.