Using first term instead of common difference
"The Difference Confusion"
The Mistake in Action
Find the nth term of 3, 7, 11, 15, ...
Wrong: nth term = $3n + 4$
Why It Happens
Students swap the roles of the first term and common difference in the formula.
The Fix
In $dn + c$:
- $d$ is the common difference (the gap between terms)
- The coefficient of $n$ is always the difference
For 3, 7, 11, 15, ...:
- Common difference = $7 - 3 = 4$
- So we start with $4n$: gives 4, 8, 12, 16, ...
- First term should be 3, but $4n$ gives 4 when $n=1$
- Adjustment: $3 - 4 = -1$
nth term = $4n - 1$
Spot the Mistake
Can you identify where this student went wrong?
Sequence: 3, 7, 11, 15, ...
nth term = $3n + 4$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: