Arithmetic sequence uniform distribution

A question is this type if and only if the discrete uniform distribution takes values in an arithmetic sequence like {a, a+k, a+2k, ...} rather than consecutive integers.

1 questions

OCR MEI Further Statistics Minor 2022 June Q6
6 The random variable \(X\) has a uniform distribution over the values \(\{ 1,4,7 , \ldots , 3 n - 2 \}\), where \(n\) is a positive integer.
  1. Determine \(\operatorname { Var } ( X )\) in terms of \(n\).
  2. Given that \(n = 100\), find the probability that \(X\) is within one standard deviation of the mean.