How to find terms and sums of sequences on the Casio fx-CG50
Σ for arithmetic and geometric sums, lists of terms, and the recursion/table mode for the nth term. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
Arithmetic and geometric series in every course, compound-interest style growth in AI, and "find the least n such that Sₙ > 1000" questions where a table of Sₙ is the quickest route.
Practise it: SL AI sequences and series · SL AA sequences and series · HL AI infinite geometric series.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Sequences and sums on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 1 (RUN-MATRIX).
- OPTN F4 (CALC) F6 (▷) F3 (Σ( ).
- In Math input mode fill the template: 3X + 2 as the term, X as the variable, 1 below and 20 above. In linear mode type Σ(3X+2, X, 1, 20). EXE.
- Geometric: Σ(5 × 0.8^(X − 1), X, 1, 10) EXE.
- For a table of terms or partial sums: MENU 8 (RECURSION), F3 (TYPE) F1 aₙ = An + B, enter aₙ, F5 (SET) for the start and end n, then F6 (TABLE). Turn on Σ Display in SHIFT MENU (SET UP) to add a Σaₙ column.
- Any letter can be the counter, but it must be the same letter in the term and in the Σ template.
- Recursion mode is also the fastest way to answer "find the smallest n such that Sₙ > 1000": look down the Σaₙ column.
Sequences and sums on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- Σ template (OS 5.x): math 0: summation Σ( … or alpha window (F2 shortcut) → Σ(. Fill in the term 3X + 2, X, 1 and 20. enter.
- Older method: 2nd stat (LIST) → MATH 5: sum( and 2nd stat → OPS 5: seq( : sum(seq(3X+2, X, 1, 20)).
- For a table of terms: mode → SEQ, then y= u(n) = 3n + 2, and 2nd graph (TABLE).
- Remember to switch mode back to FUNCTION afterwards, or your graphs disappear.
Sequences and sums on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Calculator page: templates (the key next to book) → Σ template, or menu → Calculus → Sum.
- Fill in n = 1, 20 and 3n + 2, enter.
- Lists of terms: seq(3n+2, n, 1, 20) and sum(seq(…)) also work; cumulativeSum(seq(…)) lists all the partial sums.
Worked example
(a) Find Σn=120 (3n + 2). (b) Find the sum of the first 10 terms of the geometric series 5 + 4 + 3.2 + … and its sum to infinity.
Answers (checked with Python)
(a) 670. (b) S₁₀ = Σk=110 5(0.8)k−1 = 22.3156; S∞ = 5 ÷ (1 − 0.8) = 25.
Common calculator mistakes
- Off by one: "the first 10 terms" of uₙ = 5(0.8)ⁿ⁻¹ is n = 1 to 10, but if the sequence starts at n = 0 the limits change.
- Brackets on the power: 5 × 0.8^X − 1 is not 5 × 0.8^(X − 1).
- For "least n" questions, show the two values either side (S₁₄ = 998, S₁₅ = 1021), not just the n.
- A sum to infinity only exists for |r| < 1: the calculator will happily add 100 terms of a diverging series.
Do it in Desmos
Not in the exam. Desmos is not an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- Type the Σ template: sum from n = 1 to 20 of (3n + 2).
- Make a list of terms: u = 5·0.8^(n − 1) for n = [1...10] and plot the points (n, u) to see the decay.
- total(u) adds the list: compare with the Σ.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
sum_{n=1}^{20}(3n+2)N=[1...10]U=5·0.8^{N-1}(N,U)total(U)
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.