6. Advanced Topics

Sequences — Quiz

Test your understanding of sequences with 5 practice questions.

Practice Questions

Question 1

Given an arithmetic sequence with $a_{3}=14$ and $a_{7}=26$, what is its general term $a_{n}$?

Question 2

In a geometric sequence, $a_{1}=5$ and $a_{4}=40$. What are the common ratio $r$ and the general term $a_{n}$?

Question 3

What is the sum of the first 12 terms of the arithmetic sequence $3,7,11,\dots$?

Question 4

Does the infinite geometric series with $a_{1}=9$ and common ratio $r=\tfrac{2}{3}$ converge, and if so what is its sum?

Question 5

If the partial sum of a sequence is given by $S_{n}=3n^{2}-n$, what is the nth term $a_{n}$?