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

Arithmetic Sequences

等差数列

General term, partial sums and the arithmetic mean of an arithmetic sequence, plus the index-sum property: two terms whose indices sum to the same value have the same sum.

14 real-exam questions · 5 sittings34 in mock papers26 practice

Formulas

  • Arithmetic General Term

    Formula
    an=a1+(n−1)da_{n}=a_{1}+(n-1)d
    a₁
    first term
    d
    common difference
    n
    term index (positive integer)

  • Arithmetic Series Sum

    Formula
    Sn=n(a1+an)2=na1+n(n−1)2dS_{n}=\frac{n(a_{1}+a_{n})}{2}=na_{1}+\frac{n(n-1)}{2}d

  • Arithmetic Mean

    Definition
    A=a+b2A=\frac{a+b}{2}

    Applies when：A is the arithmetic mean of a and b: a, A, b form an arithmetic sequence

  • Arithmetic Index-Sum Property

    Law
    am+an=ap+aqa_{m}+a_{n}=a_{p}+a_{q}

    Applies when：{aₙ} arithmetic and m+n = p+q

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
    If {an}\{a_n\} is an arithmetic sequence with a1=2a_1=2 and common difference d=3d=3, then a100=a_{100}= ( ).
    • A．299
    • B．305
    • C．302
    • D．298
    Show answer & solution

    Answer: A

    Answer: A a100=a1+99d=2+99×3=299a_{100}=a_1+99d=2+99\times3=299. Choose A.
    See it in the full CSCA Math December 2025 Past Paper
  2. CSCA Math January 2026 Past Paper
    Given that a=2−3a = 2 - \sqrt { 3 } and b=2+3b = 2 + \sqrt { 3 }, the arithmetic mean of aa and bb is ().
    • A．1
    • B．2
    • C．±1\pm 1
    • D．- 1
    Show answer & solution

    Answer: B

    Find the arithmetic mean of a=2−3\mathrm { a } = 2 - \sqrt { 3 } and b=2+3\mathrm { b } = 2 + \sqrt { 3 }. Arithmetic mean =(a+b)/2= ( \mathrm { a } + \mathrm { b } ) / 2. Compute a +b:(2−3)+(2+3)=4+ \mathrm { b } : ( 2 - \sqrt { 3 } ) + ( 2 + \sqrt { 3 } ) = 4. So mean =4/2=2= 4 / 2 = 2.
    Take the full CSCA Math January 2026 Past Paper — timed & graded
  3. CSCA Math April 2026 Past Paper
    If −1,a,15- 1 , a , 15 is an arithmetic sequence, then a=a =
    • A．9
    • B．5
    • C．7
    • D．11
    Show answer & solution

    Answer: C

    Middle term: a=−1+152=7a = \frac { - 1 + 15 } { 2 } = 7.
    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.

14 questions across 5 sittings1 of 5 sittings available to verify free online

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

26 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

arithmetic sequencecommon difference

Related concepts

Quadratic Functions and EquationsSolving InequalitiesGeometric Sequences