Patterns in Mathematics

What is the next number in the pattern: $3, 3, 6, 6, 9, 9, \dots$?

Which of these numbers fits the pattern $n^2$ for $n=4$?

The sequence $10, 20, 30, 40$ is a pattern of multiples of which number?

What number comes next: $6, 12, 18, 24, \dots$?

Mathematics is often called the 'Language of ______'.

In the pattern $A, B, A, B, A, B, \dots$, what will be the $101^{st}$ letter?

Observe: $1+3=4$, $1+3+5=9$, $1+3+5+7=16$. What is the sum of the first 10 odd numbers?

What is the sum of the first $5$ prime numbers?

How many zeros are at the end of the product of the first $10$ natural numbers ($10!$)?

A pattern of numbers follows the rule: Multiply by 2 and add 1. If the $1^{st}$ term is $3$, what is the $5^{th}$ term?

What is the next number in the sequence: $100, 200, 400, 800, \dots$?

Identify the next term in the pattern: $10, 10, 20, 20, 30, \dots$

Find the missing number in the pattern: $2, 4, \dots, 16, 32$.

If $1^2 = 1$, $2^2 = 4$, and $3^2 = 9$, find the value of $5^2$.

What is the sum of the $4^{th}$ and $5^{th}$ square numbers?

If the sum of the first $n$ odd numbers is $100$, what is the value of $n$?

Find the next term in the sequence: $11, 22, 33, 44, \dots$.

What is the sum of the first $50$ natural numbers?

Find the $11^{th}$ term of a pattern where the first term is $10$ and each subsequent term is $2.5$ more than the previous one.

In the sequence $1, 4, 10, 20, 35, \dots$, which represents tetrahedral numbers, find the next term.

Identify the next term in the sequence $2, 20, 200, 2000, \dots$

Complete the sequence: $1, 2, 3, 4, 5, \dots$

What is the next number in the pattern $30, 27, 24, 21, \dots$?

Identify the next term: $1, 11, 21, 31, \dots$

What is the sum of the first $20$ natural numbers ($1 + 2 + 3 + \dots + 20$)?

In the sequence of multiples of $9$ ($9, 18, 27, \dots$), what is the $9^{th}$ term?

What is the sum of the first two cube numbers?

Determine the $9^{th}$ term of the sequence $0, 7, 26, 63, 124, \dots$.

Matchstick fish patterns are created where 1 fish uses 6 sticks and 2 fish use 10 sticks. How many sticks are needed for 20 fish in a row?

Find the $15^{th}$ term in the sequence $3, 6, 11, 18, 27, \dots$.

What is the next number in the sequence: $2, 6, 10, 14, \dots$?

What is the next number in the sequence: $4, 7, 10, 13, \dots$?

Find the missing term in the sequence: $100, 80, \dots, 40, 20$.

What is the next term in the sequence: $1.1, 2.2, 3.3, 4.4, \dots$?

What is the $100^{th}$ term of the sequence $2, 4, 6, 8, \dots$?

A sequence follows the rule $n^2 + 2n$. What is the $5^{th}$ term?

What is the result of adding the $3^{rd}$ square number and the $3^{rd}$ triangular number?

If $a_n = n^2$, find the difference between $a_{21}$ and $a_{20}$.

If $a_n = 3n + 2$, find the sum of $a_{15}$ and $a_{16}$.

Observe the pattern: $1 \times 9 + 2 = 11$, $12 \times 9 + 3 = 111$, $123 \times 9 + 4 = 1111$. Find the result of $123456 \times 9 + 7$.

In a sequence of regular polygons, if the first is a square (all sides $2$ cm), the second is a pentagon (all sides $2$ cm), and the third is a hexagon (all sides $2$ cm), what is the perimeter of the third shape?

If a pattern of shapes is: $\text{Red Circle, Blue Circle, Red Circle, Blue Circle, ...}$, what is the $50$th shape?

What is the next number in the sequence: $11, 22, 33, 44, \dots$?

A line is divided into $1$ segment, then $2$, then $3$. What is the next number of segments?

A sequence of polygons starts with a triangle, then a square, then a pentagon. If the $n$th shape has $n+2$ sides, which shape number has $12$ sides?

An increasing pattern of squares: $1 \times 1, 3 \times 3, 5 \times 5, \dots$. What is the total number of unit squares in the $6$th figure?

A matchstick pattern forms the letter 'F'. Step 1 uses $4$ sticks. If each additional 'F' in the sequence uses $3$ more sticks, how many sticks are used for $20$ 'F's?

A pattern of dots is arranged in an 'X' shape. The $1^{st}$ 'X' has $5$ dots (one center, four on arms). The $2^{nd}$ 'X' has $9$ dots. The $3^{rd}$ 'X' has $13$ dots. How many dots are in the $n^{th}$ figure?

A sequence of figures: Fig $1$ is a circle, Fig $2$ is two concentric circles, Fig $3$ is three concentric circles. If the radius of the smallest circle is $1$ unit and each subsequent circle's radius increases by $1$, what is the area of the shaded region between the $9^{th}$ and $10^{th}$ circles?

How many squares of all sizes are there in a $4 \times 4$ grid pattern?

Find the next number in the sequence: $\frac{1}{2}, 1, \frac{3}{2}, 2, \dots$

If a pattern follows the rule $5n$, what is the $4^{th}$ term?

What is the next term in the sequence: $7, 17, 27, 37, \dots$?

Identify the next number in the sequence: $10, 10.5, 11, 11.5, \dots$

If the rule for a sequence is $n^2 + n$, what is the $3^{rd}$ term?

What is the next term in the sequence $100, 99, 97, 94, 90, ...$?

In the sequence $3, 8, 13, 18, ...$, which term is $48$?

If the pattern of numbers is $2, 4, 6, 8, \dots$, what is the sum of the $50^{th}$ and $51^{st}$ terms?

Find the $11^{th}$ term of a sequence where $T_n = n^2 - n$.

What is the $10^{th}$ term of the sequence $1, 3, 7, 15, 31, \dots$?