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 series (the sum of the first n terms) in 4MA1. Use the calculator to check a sum you found with the formula.
Practise it: IGCSE units (Unit 2: Sequences).
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.
Sequences and sums on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 1 (Calculate).
- SHIFT log▭ (Σ). Type 3X + 2, then 1 and 20 in the limits, =.
- Geometric: Σ with 5 × 0.8^(X − 1) from 1 to 10.
- Table of terms: MENU 9 (Table) with f(x) = 3x + 2, Start 1, End 20, Step 1.
- The Σ counter on the ClassWiz is always x.
Sequences and sums on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Calculate.
- CATALOG → Func Analysis → Summation(Σ). Type the term and the limits, EXE.
- Table of terms: the Table app with f(x) = 3x + 2.
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 allowed in IGCSE exams. Use it to learn, to check an answer and to see the graph behind a question.
- 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.
Open desmos.com/calculator (free, in any browser) 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.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- 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.