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The Formula for Any Term
The Formula for Any Term
You've spotted a pattern in a sequence: 5, 9, 13, 17... (+4 each time). But what if you needed the 100th term? You wouldn't count them all! Instead, you'd use a formula called the "nth term" that lets you find ANY term instantly. It's like having a mathematical shortcut for any position in the sequence.
Visual Guide
What is the nth term?: A formula that allows you to find any term in a sequence by substituting the position number (n)
Mathematics glossary
- What is the nth term?
- A formula that allows you to find any term in a sequence by substituting the position number (n)
Earn the mark scheme marks
Common Mistakes to Avoid
✗ Forgetting to check your answer
✓ Always substitute n=1, 2, 3 to verify
One mistake can give a wrong formula
✗ Getting the sign wrong for d
✓ Decreasing = negative d
Check: does sequence go up (+d) or down (−d)?
✗ Confusing term number with term value
✓ n is the position, the answer is the value
"5th term" means n=5, not the term = 5
Now try it yourself
Quiz · Question 1 of 11
The nth term of a sequence is 3n + 2. What is the 5th term?
Tap an answer to check it