Adding first term to dn without checking
"The First Term Fumble"
The Mistake in Action
Find the nth term of 5, 9, 13, 17, ...
Wrong: Difference = 4, first term = 5 nth term = $4n + 5$
Why It Happens
Students find the common difference correctly and then just add the first term, without checking if this actually gives the right values.
The Fix
After writing $dn$, compare it to the actual first term to find the adjustment.
Sequence: 5, 9, 13, 17, ... (difference = 4)
$4n$ gives: 4, 8, 12, 16, ... (when $n$ = 1, 2, 3, 4)
Compare first terms: sequence has 5, but $4n$ gives 4. Adjustment: $5 - 4 = 1$
nth term = $4n + 1$
Check: $4(1)+1=5$ ✓, $4(2)+1=9$ ✓
Spot the Mistake
Can you identify where this student went wrong?
Sequence: 5, 9, 13, 17, ...
Difference = 4
nth term = $4n + 5$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: