Sₙ=3ⁿ⁺¹−2k is the partial sum of a geometric sequence. Find k and aₙ.

01 / Standard#Your turn

Official paper · jm01-2023 · II.3(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Compute a₁ separately, then a₂ and a₃ by differences.

Hint 2

Use a₂²=a₁a₃.

Worked solution

k=3/2; aₙ=2·3ⁿ.

Checks and common pitfalls: The difference formula for n≥2 cannot determine a₁ without checking S₁.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The first three terms are 9−2k,18,54.
$18^2=54(9-2k)\implies k=3/2$
Identify first term 6 and ratio 3.
$a_n=6\cdot3^{n-1}=2\cdot3^n$

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

2023 JM01