BitWithBite
Mathematics Worksheet
🔁 Recurrence Relations
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After this worksheet you can
Compute terms of a recurrence.Recognise arithmetic and geometric recurrences.Work with the Fibonacci sequence.Understand the need for a base case.📚 Quick Recap
A recurrence relation defines each term of a sequence in terms of previous terms — a natural way to describe patterns that build on themselves, like the famous Fibonacci sequence.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1a(n) = a(n−1) + 4, a(1) = 5. Find a(5):
2a(n) = 2·a(n−1) + 1, a(1) = 1. Find a(4):
3Fibonacci with a(1)=1, a(2)=1. Find a(8):
4Without a base case, a recurrence:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A recurrence defines each term from terms.
6For a(n)=a(n−1)+4, a(1)=5, a(5) = .
7a(n) = a(n−1) + 4, a(1) = 5. Find a(5).
8a(n) = 2·a(n−1) + 1, a(1) = 1. Find a(4).
9Fibonacci with a(1)=1, a(2)=1. Find a(8).
🚀 Section C · Challenge ● CHALLENGE 5
10a(n) = a(n−1) − 2, a(1) = 20. Find a(6).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 previous 6 21 7 = 21 (5, 9, 13, 17, 21) 8 = 15 (1, 3, 7, 15) 9 = 21 | 10 = 10 (20, 18, 16, 14, 12, 10)