Use the first six terms to predict the limit of the sequence $ a_{n}=\frac{8 n^{3}+6}{n+3} $ (assume $ n $ begins with 1).
A) $ \frac{8}{3} $
B) 183
C) 126
D) 0
E) the sequence diverges

Question

Quizplus · Accepted Answer

To predict the limit of the sequence as $n$ approaches infinity, we examine the behavior of the sequence's formula. The dominant term in the numerator is $8n^3$ and in the denominator is $n$, making the sequence grow without bound as $n$ increases. Therefore, the sequence diverges and does not approach a finite limit.

Use the First Six Terms to Predict the Limit of the Sequence