How to find terms and sums of sequences on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II

Q: Can I use a calculator for sequences and sums in the exam?

In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.

Q: What are the fx-CG50 keystrokes for sequences and sums?

MENU 1 (RUN-MATRIX). Then OPTN F4 (CALC) F6 (▷) F3 (Σ( ). Then 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. The full steps and the other calculators are in the keystrokes section above.

Q: Does this work on other calculators?

Yes. This page has keystrokes for the 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.

Q: 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 exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.

On the fx-CG50: MENU → 1 (RUN-MATRIX) → OPTN → F4 (CALC) → F6 (▷) → F3 (Σ().On the TI-84 Plus CE: math → 0: summation.

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.

Calculators: Casio fx-CG50 (OS 3.80) · TI-84 Plus CE (OS 5.8.x) · TI-Nspire CX II (OS 6.x). Checked September 2026.

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.

Which IB course and paper

Course	GDC papers	What you use it for
AA SL	Paper 2 (Paper 1 is calculator-free)	Arithmetic and geometric sums, sums to infinity, and "least n" questions.
AA HL	Papers 2 and 3 (Paper 1 is calculator-free)	As SL.
AI SL	Papers 1 and 2	Arithmetic and geometric sums and the least n for which Sₙ passes a value.
AI HL	Papers 1, 2 and 3	As SL, plus sums to infinity.

A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.

Topic notes: Arithmetic sequences and series (AI SL) · Geometric sequences and compound interest (AI SL) · Arithmetic and geometric sequences (AA SL) · Sequences, series, and the sum to infinity (AI HL) · Sequences, series, and induction proofs (AA HL).

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).

Key sequence, from the steps below.

Watch the key presses on the fx-CG5016 presses, one at a time

The walkthrough needs JavaScript. The same key presses are in the numbered steps below.

Watch every key press on YouTube: the fx-CG50 playlist

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.

Schematic Casio fx-CG50 screen for sequences and sums: the RUN-MATRIX (Math) screen showing Σ(3X+2) X=1..20, 670, Σ(5×0.8^(X−1)) X=1..10, with FMin, FMax, Σ(, logab, Int÷, ▷ on the F-keys — Schematic fx-CG50 screen (our drawing, not a photo); the bottom row is what F1–F6 do here.

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.

For teachers: Show on the board Print a keystroke card Teaching GDC skills

Worked example

(a) Find Σ_n=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 = Σ_k=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 IB-style sequences and series questions. Free to try, no sign-up.

Try a sequences and series question

Want your scores kept? Join free (no card) · Sign in

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.
A number of terms (or years) must be a whole number: if the table shows S₁₄ < 1000 < S₁₅, the answer is n = 15, with both sums written down.
Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).

If you get an error

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.

Every error message explained, calculator by calculator →

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.

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?

In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.

What are the fx-CG50 keystrokes for sequences and sums?

MENU 1 (RUN-MATRIX). Then OPTN F4 (CALC) F6 (▷) F3 (Σ( ). Then 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. The full steps and the other calculators are in the keystrokes section above.

Does this work on other calculators?