Sequences
2 marks · NormalGiven the sequence 4, 9, 16, 25, 36, ..., write a formula for the nth term.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
a_n = n^2 + 3
Also accept: n^2 + 3; a_n = n^2 + 3
Common mistakes: Writing n^2 instead of n^2 + 3
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Spots correct pattern (square numbers plus 3) or relates terms to n.
A1 · 1 mark · Writes correct nth term formula a_n = n^2 + 3 (or equivalent).
Worked solution
First term: 4 (when n=1); Second term: 9 (n=2); etc. Compare with n^2: 1^2=1, 2^2=4, 3^2=9, etc.
Wait, let's list values:
| n | Term | n^2 |
|---|---|---|
| 1 | 4 | 1 |
| 2 | 9 | 4 |
| 3 | 16 | 9 |
| 4 | 25 | 16 |
| 5 | 36 | 25 |
The terms are exactly (n+1)^2, since 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36.
So the nth term is (n + 1)^2.