Patterns in Mathematics: Solving Pattern-Based Questions: 18 flashcards
All 18 flashcards from this kit, free and with no sign-up.
1. What does it mean to solve a patterns question?
Show the answer
Find the rule that generates every term, then prove it works for all given terms.
2. Why label terms $T_1, T_2, T_3, \dots$ before analysing?
Show the answer
Labels let you refer to positions precisely and connect terms to their index $n$.
3. How are first differences found?
Show the answer
Subtract each term from the next: $T_2 - T_1$, $T_3 - T_2$, and so on.
4. What do constant first differences tell you?
Show the answer
The pattern is arithmetic (linear): each term is obtained by adding a fixed number $d$.
5. What do constant second differences tell you?
Show the answer
The pattern is quadratic; the rule involves $n^2$.
6. How do you test for a geometric pattern?
Show the answer
Divide each term by the previous one; if the ratio is constant, it is geometric.
7. Formula for the $n$-th term of an arithmetic sequence?
Show the answer
$T_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.
8. What are the first differences of $1, 4, 9, 16, 25$?
Show the answer
$3, 5, 7, 9$ — they increase by $2$ each time.
9. What are the second differences of $1, 4, 9, 16, 25$?
Show the answer
All equal to $2$, confirming a quadratic pattern.
10. Why must a rule be tested against every given term?
Show the answer
A rule that fails even one term is not the correct rule.
11. What is the rule for $5, 9, 13, 17, \dots$?
Show the answer
Add $4$ each time; $T_n = 4n + 1$.
12. What is the rule for $3, 6, 12, 24, \dots$?
Show the answer
Multiply by $2$ each time; geometric with ratio $2$.
13. How does the difference-table method help?
Show the answer
It reveals the pattern type even when you do not recognise the sequence.
14. Why is pattern recognition the foundation of algebra?
Show the answer
Writing a rule compactly is the same skill as writing an algebraic expression.
15. What is the real answer to a 'find the next term' question?
Show the answer
The rule that produces it — the next term is a consequence of the rule.
16. What is the common mistake with $2, 4, 8, \dots$?
Show the answer
Assuming 'add $2$' from the first two terms; the third term shows it is 'multiply by $2$'.
17. When might you need both difference and ratio checks?
Show the answer
For mixed patterns where neither first differences nor ratios are constant on their own.
18. What habit do pattern questions train?
Show the answer
Testing a claim against evidence — the same habit proof requires.
Your notes can be a kit like these
Every kit here was made from real study material. Point Veda at a chapter, a PDF, a photo or a link and get notes, flashcards, practice MCQs, games and a scored test — free, in 42 languages.
- Chapter notes
- Flashcards
- Practice MCQs
- Scored tests
- Exam prep
Get Veda free See what students get
Free to start · No ads · Works in 42 languages