$\text { Find the following limit of the sequence as } n \text { approaches infinity, if it exists. }$

question 25

Multiple Choice

$\text { Find the following limit of the sequence as } n \text { approaches infinity, if it exists. }$ $a_{n}=\frac{1}{n}\left(n+\frac{3}{n}\left[\frac{n(n+1) }{5}\right]\right)$

• A) \( \frac{3}{5} \)
• B) \( \frac{13}{5} \)
• C) \( \frac{8}{5} \)
• D) \( \frac{9}{5} \)
• E) The limit does not exist.

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Definitions:

Median

The middle value in a list of numbers, which separates the higher half of the data sample from the lower half.

Percentile Points

Percentile points are values that divide a set of observations into 100 equal parts, indicating the percentage of data points that fall below a certain value.

Q1

The first quartile in a data set, representing the median of the lower half of the data set, or the 25th percentile.

Skew

A measure of the asymmetry or deviation from symmetry in a distribution of data, which can be positive or negative.