IB — mathsStandard1 min read

Arithmetic Sequences and Series

Master arithmetic sequences and series for IB Maths. Find nth terms, partial sums, and solve application problems.

Tutor AI Team
Tutor AI Team

Arithmetic sequences have a constant difference between consecutive terms. They appear in Topic 1 (Number and Algebra) of both IB Math AA and AI.

Core Formulas

un=u1+(n−1)du_n = u_1 + (n-1)d — nth term

Sn=n2(2u1+(n−1)d)=n2(u1+un)S_n = \frac{n}{2}(2u_1 + (n-1)d) = \frac{n}{2}(u_1 + u_n) — sum of first nn terms

Worked Example: Example 1

Problem

u1=5u_1 = 5, d=3d = 3. Find u20u_{20} and S20S_{20}. u20=5+19(3)=62u_{20} = 5 + 19(3) = 62. S20=202(5+62)=670S_{20} = \frac{20}{2}(5 + 62) = 670.

Solution

Worked Example: Example 2

Problem

u5=17u_5 = 17, u12=38u_{12} = 38. Find u1u_1 and dd. u12−u5=7d=21u_{12} - u_5 = 7d = 21 → d=3d = 3. u1=17−4(3)=5u_1 = 17 - 4(3) = 5.

Solution

IB Exam Tips

  • Formulas are in the data booklet — know how to use them.
  • Show clear substitution for method marks.
  • Watch for sequences starting at n=0n = 0 vs n=1n = 1.

Practice Problems

    1. u1=2u_1 = 2, d=5d = 5. Find S15S_{15}.
    1. S10=155S_{10} = 155 and u1=2u_1 = 2. Find dd.
    1. How many terms of 3, 7, 11, ... are needed for Sn>500S_n > 500?

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Key Takeaways

  • ✓

    un=u1+(n−1)du_n = u_1 + (n-1)d. Sn=n2(u1+un)S_n = \frac{n}{2}(u_1 + u_n).

  • ✓

    Two equations needed to find both u1u_1 and dd.

Tags:
#ib#maths#algebra#sequences#arithmetic

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