An arithmetic sequence satisfies a₂=3 and a₂₀=39. Find its general term.

01 / Standard#Your turn

a_2=3,\quad a_{20}=39

Official paper · jm01-2021 · II.4(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

There are eighteen common differences between the two given terms.

Hint 2

Recover the first term after finding the common difference.

Worked solution

aₙ=2n−1.

Checks and common pitfalls: The index difference is 18, not 19 or 20.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Compute the common difference.
$d=(39-3)/(20-2)=2$
Find the first and general terms.
$a_1=3-2=1;\quad a_n=1+2(n-1)=2n-1$

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

2021 JM01