This deep dive covers Worked Example 1: Basketball Heights within Quadratic Sequences for GCSE Mathematics. Revise Quadratic Sequences in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 7
Practice
12 questions
Recall
22 flashcards
Worked Example 1: Basketball Heights
Problem: Find the nth term of the sequence 2, 5, 10, 17, 26, ...
Step 1: First differences
| Terms: | 2 | 5 | 10 | 17 | 26 |
| 1st differences: | 3 | 5 | 7 | 9 |
Step 2: Second differences
| 1st differences: | 3 | 5 | 7 | 9 |
| 2nd differences: | 2 | 2 | 2 |
Step 3: Find 'a'
a = ½ × 2 = 1, so we have n²
Step 4: Compare with n²
| n: | 1 | 2 | 3 | 4 | 5 |
| Original: | 2 | 5 | 10 | 17 | 26 |
| n²: | 1 | 4 | 9 | 16 | 25 |
| Difference: | 1 | 1 | 1 | 1 | 1 |
Step 5: Complete formula
The difference is constant = 1, so the formula is:
nth term = n² + 1
Check: When n = 3: 3² + 1 = 9 + 1 = 10 ✓