Find the general term of an arithmetic sequence with a₅=44 and S₅=140.

01 / Standard#Your turn

Official paper · jm01-2026 · II.3(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express a₅ in terms of the first term and common difference.

Hint 2

Use the first-plus-last form of the sum.

Worked solution

Solve the two linear constraints.
$a_1+4d=44,\quad\frac52(a_1+44)=140\implies a_1=12,\ d=8$
Substitute into the nth-term formula.
$a_n=12+8(n-1)=8n+4$

aₙ=8n+4 for n≥1.

Checks and common pitfalls: The fifth term is four differences after the first.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Solve the two linear constraints.
$a_1+4d=44,\quad\frac52(a_1+44)=140\implies a_1=12,\ d=8$
Substitute into the nth-term formula.
$a_n=12+8(n-1)=8n+4$

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

2026 JM01