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Next exam on November 14 – 15, 2026:
All concepts

Geometric Sequences

等比数列

General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.

10 real-exam questions · 5 sittings28 in mock papers12 practice

Formulas

  • Geometric General Term

    Formula
    an=a1q n−1a_{n}=a_{1}q^{\,n-1}

    Applies when：a₁ ≠ 0, q ≠ 0

    a₁
    first term (a₁ ≠ 0)
    q
    common ratio (q ≠ 0)

  • Geometric Series Sum

    Formula
    Sn={na1,q=1a1(1−qn)1−q,q≠1S_{n}=\begin{cases}na_{1}, & q=1\\[4pt] \dfrac{a_{1}\left(1-q^{n}\right)}{1-q}, & q\ne 1\end{cases}

  • Geometric Mean

    Definition
    G2=abG^{2}=ab

    Applies when：G is the geometric mean of a and b; requires ab > 0, G = ±√(ab)

How the real exam tests it

Questions from real CSCA papers that test this concept. Work each one out before you open the answer.

  1. CSCA Math December 2025 Past Paper
    The first three terms of a geometric sequence are 1, 2, 4. Its general term is ( ).
    • A．an=2na_n=2^n
    • B．an=2n−1a_n=2^{n-1}
    • C．an=8a_n=8
    • D．an=2na_n=2n
    Show answer & solution

    Answer: B

    Answer: B The sequence has first term 1 and common ratio 2, so an=2n−1a_n=2^{n-1}. Choose B.
    See it in the full CSCA Math December 2025 Past Paper
  2. CSCA Math March 2026 Past Paper
    In a geometric sequence {an}\left\{ \mathrm { a } _ { \mathrm { n } } \right\}, if a1=4\mathrm { a } _ { 1 } = 4 and a4=32\mathrm { a } _ { 4 } = 32, then a3=\mathrm { a } _ { 3 } =
    • A．8
    • B．16
    • C．- 8
    • D．- 16
    Show answer & solution

    Answer: B

    a4=a1⋅q3=4q3=32a _ { 4 } = a _ { 1 } \cdot q ^ { 3 } = 4 q ^ { 3 } = 32, so q=2q = 2. Then a3=4×22=16a _ { 3 } = 4 \times 2 ^ { 2 } = 16.
    Take the full CSCA Math March 2026 Past Paper — timed & graded
  3. CSCA Math April 2026 Past Paper
    For geometric sequence a1=−48,a4=6a _ { 1 } = - 48 , a _ { 4 } = 6, the common ratio is
    • A．−12- \frac { 1 } { 2 }
    • B．- 2
    • C．12\frac { 1 } { 2 }
    • D．2
    Show answer & solution

    Answer: A

    a4=a1q3:6=−48q3⇒q3=−18⇒q=−12a _ { 4 } = a _ { 1 } q ^ { 3 } : 6 = - 48 q ^ { 3 } \Rightarrow q ^ { 3 } = - \frac { 1 } { 8 } \Rightarrow q = - \frac { 1 } { 2 }.
    Take the full CSCA Math April 2026 Past Paper — timed & graded

Real-exam evidence

Recorded past-paper appearances are listed below; online verification is labelled separately.

10 questions across 5 sittings1 of 5 sittings available to verify free online
  • CSCA Math June 2026 Past Paper4 questionsreading page not yet public
  • CSCA Math April 2026 Past Paper2 questionsreading page not yet public
  • CSCA Math March 2026 Past Paper2 questionsreading page not yet public
  • CSCA Math January 2026 Past Paper1 questionreading page not yet public
  • CSCA Math December 2025 Past Paper1 questionView question 23 and answer free (full paper)

28 questions across 15 mock papers — our own papers, so a coverage signal rather than real-exam evidence

12 related practice questions availablePractise free: Sequence

Sitting evidence comes from the CSCA past papers on record; questions whose original paper is missing are excluded, and sprint papers are deliberately not counted.

Glossary

geometric sequence

Related concepts

Quadratic Functions and EquationsSolving InequalitiesArithmetic Sequences