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

The sequence $a_n = \frac{8n^3 + 6}{n + 3}$ simplifies to $8n^2 - 24n + 72 - \frac{222}{n + 3}$ as $n$ becomes very large. The dominant term here is $8n^2$, which grows without bound as $n$ increases. Therefore, the sequence does not approach a finite limit, indicating divergence.

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