🎯 What Is the “Nth Term”?
The nth term tells you the rule of the sequence — a formula you can use to find any number in the pattern.
Think of it as a magic machine: put in n, get the number in the sequence!
🔢 Step 1: Find the Difference
Check how much the sequence goes up each time.
Example 1:
3, 7, 11, 15, ___
Differences: +4 each time.
3, 7, 11, 15, ___
Differences: +4 each time.
So the pattern grows by 4.
🧮 Step 2: Build the Base Formula
If the difference is d, the start of your rule is:
d × n
Sequence: 3, 7, 11, 15
Difference = 4 → start with 4n.
Difference = 4 → start with 4n.
🎁 Step 3: Adjust with a Constant
Compare your formula with the real sequence.
For n = 1:
4n = 4 → but the sequence starts at 3.
So we need -1.
4n = 4 → but the sequence starts at 3.
So we need -1.
Final Rule: 4n – 1
✔️ Step 4: Check Your Formula
For n=3:
4(3) – 1 = 12 – 1 = 11 ✓
4(3) – 1 = 12 – 1 = 11 ✓
🌈 Full Example Set (With Answers)
Example A:
5, 9, 13, 17
Difference: +4 → start with 4n
4n gives 4,8,12,16
Original is 1 more → nth term = 4n + 1
5, 9, 13, 17
Difference: +4 → start with 4n
4n gives 4,8,12,16
Original is 1 more → nth term = 4n + 1
Example B:
2, 6, 10, 14
Difference: +4 → start with 4n
4n = 4,8,12,16
Sequence is 2 less → nth term = 4n – 2
2, 6, 10, 14
Difference: +4 → start with 4n
4n = 4,8,12,16
Sequence is 2 less → nth term = 4n – 2
Example C:
7, 12, 17, 22
Difference: +5 → start with 5n
5n = 5,10,15,20
Sequence is 2 more → nth term = 5n + 2
7, 12, 17, 22
Difference: +5 → start with 5n
5n = 5,10,15,20
Sequence is 2 more → nth term = 5n + 2
🤖 Mini Nth-Term Calculator
Enter a difference and starting number: