Fibonacci-Type Sequence

A sequence where each term is the sum of the two preceding terms.

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A sequence where each term is the sum of the two preceding terms.

A Fibonacci-type sequence (also called a recursive additive sequence) is one where each term equals the sum of the two terms before it. The classic Fibonacci sequence starts with 0 and 1, but any two starting numbers create a valid Fibonacci-type sequence. These patterns appear in nature (flower petals, pinecones, shells) and have fascinating mathematical properties.

aₙ = aₙ₋₁ + aₙ₋₂

1, 1, 2, 3, 5, 8, 13, 21... (classic Fibonacci)
2, 5, 7, 12, 19, 31... (starts with 2 and 5)
1, 3, 4, 7, 11, 18... (Lucas numbers)

How to recognize it

Check if each term equals the sum of the two before it
Look for accelerating growth that's not purely multiplicative
The differences between terms will themselves form a pattern

Common mistakes

Only expecting the classic 1, 1, 2, 3, 5... pattern
Confusing with simple addition sequences
Not checking multiple pairs of consecutive sums

Step-by-step walkthrough

Find the next term: 1, 1, 2, 3, 5, 8, ?

Check if each term = sum of previous two: 1+1=2 ✓
Continue checking: 1+2=3 ✓, 2+3=5 ✓, 3+5=8 ✓
This is Fibonacci-type. Add the last two terms
The next term is 13

Answer: 13

Practice guidance

Number Sequences