4. Algebraic Foundations

Patterns — Quiz

Test your understanding of patterns with 5 practice questions.

Practice Questions

Question 1

A sequence is defined by the recursive rule $a_n = a_{n-1} + 2n$, with $a_1 = 1$. What is the $4^{th}$ term of this sequence?

Question 2

Consider a pattern where the number of blocks in each figure follows the rule $B_n = n^2 + n + 1$, where $n$ is the figure number. How many blocks will be in the $6^{th}$ figure?

Question 3

A functional rule is given by $f(x) = -2x^2 + 5x - 3$. What is the value of $f(-1)$?

Question 4

A pattern of tiles is arranged in rows. The first row has 2 tiles, the second row has 5 tiles, the third row has 10 tiles, and the fourth row has 17 tiles. If this pattern continues, how many tiles will be in the $8^{th}$ row?

Question 5

A sequence is defined by the rule $a_n = (-1)^{n+1} \cdot (n+1)^2$. What is the sum of the first three terms of this sequence?