How to find terms and sums of sequences on a Casio ClassWiz or fx-CG50
On the fx-991EX: MENU → 1 (Calculate) → SHIFT x (Σ□).On the fx-991CW: CATALOG → Function Analysis → Summation(Σ).
Σ for arithmetic and geometric sums, lists of terms, and the recursion/table mode for the nth term. Exact keystrokes for the Casio ClassWiz first (the fx-991EX and fx-991CW have different menus, so each has its own tab), then the graphic 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-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
Watch the key presses on the fx-991EX10 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- MENU 1 (Calculate).
- SHIFT x (Σ□). Type 3X + 2 (X is ALPHA )), then 1 and 20 in the limits with ►, =.
- 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 → Function Analysis → Summation(Σ). Type the term and the limits, EXE.
- Table of terms: the Table app with f(x) = 3x + 2, Start 1, End 20, Step 1.
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 a different model: check the exam rules before using one).
- Calculator page: templates (the key next to book) → Σ template, or menu → Calculus → Sum.
- Fill in n = 1, 20 and 3n + 2, enter.
- Geometric: the same Σ template with 5·0.8^(n−1), n = 1 and 10, enter.
- Lists of terms: seq(3n+2, n, 1, 20) and sum(seq(…)) also work; cumulativeSum(seq(…)) lists all the partial sums.
For teachers: Show on the board Print a keystroke card Teaching GDC skills
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.
Now try it on an exam-style question
Use the keystrokes above on IGCSE-style sequences questions. Free to try, no sign-up.
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.
If you get an error
fx-991EX: Math ERROR, Syntax ERROR
Math ERROR A result, or a value you typed, is outside the range the calculator can handle, or you asked for something mathematically impossible, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check the values you typed, use fewer digits and try again. If a variable is the input to a function, make sure its value is one the function accepts.
Syntax ERROR There is a problem with the format of the calculation. In Matrix and Vector calculations it also appears when the sizes do not suit the operation. Check: A missing or extra bracket, or two operation signs in a row. With matrices or vectors: adding a 2 × 2 to a 3 × 3, or a product whose sizes do not match. Fix: Casio's advice: make the corrections. For matrices and vectors, check the size you set for each one.
fx-991CW: Math ERROR, Syntax ERROR
Math ERROR A result, or a value you typed, is outside the range the calculator can handle, or you asked for something mathematically impossible, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check the values you typed, use fewer digits and try again. If a variable is the input to a function, make sure its value is one the function accepts.
Syntax ERROR There is a problem with the format of the calculation: it is typed in a form the calculator cannot read. Check: A missing or extra bracket, two operation signs in a row, or a function with nothing after it. Fix: Casio's advice: make the corrections and try again.
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:SYNTAX
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
TI-Nspire CX II: Domain error, Syntax error
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
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)
Questions
Can I use a calculator for sequences and sums in the exam?
On Pearson Edexcel International GCSE Maths A (4MA1), yes: Paper 1H and Paper 2H both allow a calculator with no CAS. On Cambridge IGCSE 0580 (from 2025), Papers 1 and 2 are non-calculator, and the syllabus says you should have a scientific calculator for Papers 3 and 4.
What are the fx-991EX keystrokes for sequences and sums?
MENU 1 (Calculate). Then SHIFT x (Σ□). Type 3X + 2 (X is ALPHA )), then 1 and 20 in the limits with ►, =. Then Geometric: Σ with 5 × 0.8^(X − 1) from 1 to 10. The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-991EX ClassWiz, Casio fx-991CW ClassWiz, Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer to the accuracy the question asks for (often 3 significant figures). Keep full accuracy in later parts.
More calculator skills
Sources
- 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).
- 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 models 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. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.