Calculate the next two terms of the recurrence.

01 / Standard#Your turn

f(x)=\frac{3x}{x+3},\quad x_1=\frac32,\quad x_n=f(x_{n-1})

Official paper · jm01-2026 · II.5(a)(i) · PDF 5

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Substitute x₁ into f.

Hint 2

Then use the newly obtained x₂.

Worked solution

x₂=1, x₃=3/4.

Checks and common pitfalls: The recurrence iterates f; it does not substitute the index n into f.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Evaluate the first substitution.
$x_2=\frac{3(3/2)}{3/2+3}=1$
Apply the same function once more.
$x_3=\frac{3\cdot1}{1+3}=\frac34$

Think first. Reveal a hint when the class is ready.

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