Find the next three terms of the sequence; 0, 1, 1, 2, 3, 5, 8...

Analyze the question: We need to find the pattern in 0, 1, 1, 2, 3, 5, 8... and continue it for three more terms.

Concept: This is the famous Fibonacci sequence. Each term is the sum of the two terms before it:

Tₙ = Tₙ₋₁ + Tₙ₋₂

Check the pattern:

• 0 + 1 = 1
• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8

The rule works for every term.

Find the next three terms:

• 5 + 8 = 13
• 8 + 13 = 21
• 13 + 21 = 34

So the sequence continues: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

Check the options:

• A (13, 19, 23): 8 + 13 = 21, not 19. Wrong.
• B (9, 11, 13): These do not follow the rule. Wrong.
• C (11, 15, 19): Wrong.
• D (13, 21, 34): Matches our working. Correct.

Tip: When a sequence is neither an arithmetic progression (constant difference) nor a geometric progression (constant ratio), check whether each term is the sum of the previous two. If it is, you are looking at a Fibonacci sequence. Learn the early terms by heart: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...