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
Checking Σ notation answers, geometric series and sums to infinity, and "the least n for which …" questions (a table of Sₙ, then justify with two values).
Practise it: Sequences and 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.
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 A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- 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.
- 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.