01 Key Concepts
Arithmetic Sequence
Each term is found by adding a constant (the common difference, d) to the previous term.
Arithmetic Sequence Formula
The nth term is a(n) = a(1) + (n-1)*d, where a(1) is the first term.
Geometric Sequence
Each term is found by multiplying the previous term by a constant (the common ratio, r).
Geometric Sequence Formula
The nth term is a(n) = a(1) * r^(n-1).
Finding the Common Difference or Ratio
For arithmetic: subtract any term from the next one. For geometric: divide any term by the previous one.
02 Key Formulas
- Arithmetic: a(n) = a(1) + (n-1)*d
- Geometric: a(n) = a(1) * r^(n-1)
03 Solved Examples
Example 1 Find the 10th term of the arithmetic sequence 3, 7, 11, 15, ...
- Identify a(1)=3 and d=4 (each term adds 4).
- Apply the formula: a(10) = 3 + (10-1)*4 = 3 + 36.
Answer: a(10) = 39
Example 2 Find the 6th term of the geometric sequence 2, 6, 18, 54, ...
- Identify a(1)=2 and r=3 (each term multiplies by 3).
- Apply the formula: a(6) = 2 * 3^(6-1) = 2 * 3^5.
- 3^5 = 243.
- 2 * 243.
Answer: a(6) = 486
Example 3 Find the common ratio of the sequence 100, 50, 25, 12.5, ...
- Divide any term by the previous one: 50/100 = 0.5.
- Check with another pair: 25/50 = 0.5, consistent.
Answer: r = 0.5
04 Practice Questions
1Find the 5th term of 2, 5, 8, 11, ... (arithmetic).
14
2Find the common difference of 10, 8, 6, 4, ...
-2
3Find the 4th term of 3, 6, 12, 24, ... (geometric).
24
4Find the common ratio of 5, 15, 45, 135, ...
3
5Find the 10th term of the arithmetic sequence with a(1)=1, d=2.
19
📄 Sequences — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.