How can I tell whether an IB Maths AA sequence is arithmetic or geometric?

Calculate the difference between consecutive terms and then, where the terms are non-zero, calculate their ratio. A constant difference identifies an arithmetic sequence, while a constant ratio identifies a geometric sequence. Do not classify a sequence simply because its terms increase or decrease, since either type can do this. In contextual questions, constant additions usually indicate arithmetic change, while repeated percentage changes indicate geometric change. When reviewing a worked solution, focus on the evidence used to classify the sequence before any formula is selected.

What is the difference between uₙ and Sₙ in sequences and series?

uₙ is the value of the nth individual term, whereas Sₙ is the sum of the first n terms. For the sequence 3, 6, 9, 12, u₄ = 12, but S₄ = 3 + 6 + 9 + 12 = 30. Questions asking for a particular payment, height, or yearly value usually require a term formula. Questions asking for a total, cumulative amount, or combined distance usually require a sum formula. Writing “term” or “sum” beside the target before calculating prevents one of the most frequent formula-choice errors.

When can I use the infinite geometric series formula in IB Maths AA?

You may use S∞ = u₁/(1 - r) only when the common ratio satisfies |r| < 1. This condition means the terms approach zero and the partial sums approach a finite limit. A ratio such as -0.5 is valid because its absolute value is below one, even though the terms alternate in sign. Ratios such as 1.2, -1, or 2 do not produce a convergent infinite geometric series. In an exam solution, calculate or state the ratio and verify the condition before applying the formula.

Why does the nth-term formula contain n minus 1?

The exponent or multiplier count is n - 1 because no change has occurred at the first term. Moving from u₁ to u₂ involves one addition of d or one multiplication by r. Reaching uₙ from u₁ therefore requires n - 1 transitions. This gives uₙ = u₁ + (n - 1)d for arithmetic sequences and uₙ = u₁rⁿ⁻¹ for geometric sequences. Writing out the first three terms is an effective way to confirm the indexing when a context uses time zero.

How should I round the number of terms in a threshold problem?

Do not round mechanically, because the required integer depends on the wording of the question. If you obtain n > 8.2 and need the first whole period when a value exceeds a threshold, the answer is normally n = 9. If the question asks how many complete periods remain below a limit, the appropriate answer may instead be 8. Substitute the neighbouring integers into the original model to verify which one satisfies the condition. Your final statement should include the unit and explain the meaning of the selected integer.

Are sequences and series formulas provided in the IB Maths AA examination?

The standard arithmetic and geometric term and sum formulas are included in the Mathematics: Analysis and Approaches formula booklet. Students are provided with a clean copy of the booklet under the relevant examination arrangements. However, the booklet does not decide which model applies or explain how the variables correspond to a particular context. You must still distinguish uₙ from Sₙ, determine d or r, and check the convergence condition for an infinite series. Regular practice with the booklet helps you locate formulas quickly while concentrating on interpretation and algebra.

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IB Maths AA Sequences & Series: Mistakes and Fixes

Q: Why does the nth-term formula contain n minus 1?

The exponent or multiplier count is n - 1 because no change has occurred at the first term. Moving from u₁ to u₂ involves one addition of d or one multiplication by r. Reaching uₙ from u₁ therefore requires n - 1 transitions. This gives uₙ = u₁ + (n - 1)d for arithmetic sequences and uₙ = u₁rⁿ⁻¹ for geometric sequences. Writing out the first three terms is an effective way to confirm the indexing when a context uses time zero.

Q: How should I round the number of terms in a threshold problem?

Do not round mechanically, because the required integer depends on the wording of the question. If you obtain n > 8.2 and need the first whole period when a value exceeds a threshold, the answer is normally n = 9. If the question asks how many complete periods remain below a limit, the appropriate answer may instead be 8. Substitute the neighbouring integers into the original model to verify which one satisfies the condition. Your final statement should include the unit and explain the meaning of the selected integer.

• 5 Aug 2026•11

IB Maths AA Sequences & Series: Mistakes and Fixes

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IB Maths AA Sequences & Series: Mistakes and Fixes | RevisionDojo

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IB Maths AA Sequences & Series: Mistakes and Fixes

• 5 Aug 2026•11

Errors in IB Maths AA sequences and series usually come from choosing the wrong model, confusing a term with a sum, mishandling indices, or using an infinite-series formula without checking convergence. These problems are highly fixable because the same errors recur across exam-style questions. The most effective correction is to attempt a question, compare every line with a worked video solution, and identify the first point where your reasoning diverged.

The current Mathematics: Analysis and Approaches course includes arithmetic and geometric sequences, finite series, sigma notation, infinite geometric series, and financial applications such as compound interest and depreciation. These ideas are part of Topic 1: Number and Algebra for both SL and HL.

Essential formulas and distinctions

A sequence is an ordered list of terms, while a series is the result of adding terms. Therefore, uₙ represents a term and Sₙ represents a sum.

Type	Term formula	Sum formula	Key condition
Arithmetic	`uₙ = u₁ + (n - 1)d`	`Sₙ = n/2[2u₁ + (n - 1)d]`	Consecutive terms have constant difference `d`
Geometric	`uₙ = u₁rⁿ⁻¹`	`Sₙ = u₁(1 - rⁿ)/(1 - r)`	Consecutive non-zero terms have constant ratio `r`
Infinite geometric	Not applicable	`S∞ = u₁/(1 - r)`	Valid only when **

These formulas appear in the Mathematics: Analysis and Approaches formula booklet. You should know how to select and use them rather than relying on memorization alone.

IB Maths AA sequences and series common mistakes

Common mistake	Why it happens	Practical fix using worked solutions
Assuming every pattern is arithmetic	Students look at the size of the terms rather than the operation connecting them.	In the first line, calculate both `u₂ - u₁` and `u₂/u₁`. When reviewing a video solution, pause before the classification and predict which test will be used.
Confusing `uₙ` with `Sₙ`	Words such as “total,” “altogether,” and “after n payments” are overlooked.	Rewrite the target as either one term or a sum of terms before selecting a formula. Check whether the worked solution defines `uₙ` or `Sₙ`.
Using `n` instead of `n - 1`	Students forget that the first term has undergone zero changes.	Write the first three generated terms: `u₁`, `u₁ + d`, `u₁ + 2d` or `u₁`, `u₁r`, `u₁r²`. Compare this setup with the solution before substituting values.
Using `S∞` for any infinite-looking question	“Continues forever” is mistaken for “has a finite sum.”	Find `r` and explicitly write **
Losing signs when `r` is negative	Powers of a negative ratio alternate between positive and negative.	Keep negative ratios in brackets, such as `(-0.4)ⁿ`. Pause the video before simplification and calculate the sign independently.
Misreading sigma limits	Students assume the upper limit equals the number of terms.	Use number of terms = upper limit - lower limit + 1. Expand the first two and final terms, then compare them with the video expansion.
Modelling percentages incorrectly	A percentage change is entered as the percentage itself rather than a multiplier.	Convert growth by `p%` to `r = 1 + p/100` and depreciation to `r = 1 - p/100`. Check how the worked solution defines time zero and the first modelled period.
Rounding `n` without interpreting it	A decimal answer from logarithms is treated as an ordinary numerical result.	Translate the inequality back into context. If a threshold is first exceeded after `8.2` periods, test nearby integers and usually select `n = 9`.

Formula choice before calculation

A reliable exam method is to label the information before touching the calculator:

Write u₁, d or r, and the required quantity.
Decide whether the question asks for uₙ, Sₙ, or S∞.
State the relevant formula symbolically.
Substitute values with brackets around negative numbers.
Interpret the result in the context of the question.

For example, suppose a machine is worth $18,000 and depreciates by 12% each year. The geometric multiplier is r = 0.88, not 0.12. If the initial value is defined as u₁, then uₙ = 18000(0.88)ⁿ⁻¹; if it is defined at time t = 0, a model such as V(t) = 18000(0.88)ᵗ is more natural. Both can describe the situation, but mixing their indexing creates an off-by-one error.

Targeted practice is available in RevisionDojo’s arithmetic sequences and series Questionbank, geometric sequences and series Questionbank, and financial applications Questionbank.

Sigma notation and indexing errors

Consider Σ(3k - 1) from k = 2 to k = 6. The terms are 5 + 8 + 11 + 14 + 17, so there are five terms, not six. Changing the dummy variable from k to j does not change the sum, but changing the limits does.

When converting a written series into sigma notation, verify three points:

Substituting the lower limit produces the first required term.
Substituting the next integer produces the second term.
Substituting the upper limit produces the final term.

This three-term check catches most indexing mistakes faster than manipulating the complete expression.

How to review video solutions effectively

Watching a solution passively can create familiarity without improving independent performance. Use the arithmetic sequences video solutions as a line-by-line diagnostic tool instead.

For each question:

Attempt it fully without assistance.
Watch only until the presenter classifies the sequence and identifies the target.
Pause and complete the next step yourself.
Compare the first incorrect line, not only the final answer.
Record the error under a category such as classification, indexing, algebra, convergence, or interpretation.
Reattempt the question after one or two days without replaying the solution.

The wider IB Mathematics AA resource hub also organizes notes, questions, and videos by syllabus area. Jojo AI can help explain why a particular setup fails, but you should still write and check the complete mathematical argument yourself.

Exam technique and calculator use

According to the official IB Mathematics AA subject brief, Paper 1 does not allow technology, while Paper 2 allows technology; HL Paper 3 also allows technology. However, calculator access does not replace mathematical setup. A calculator output without a recognizable sequence model may not communicate the reasoning needed for method credit.

Unless a question specifies otherwise, official specimen-paper instructions require numerical answers to be exact or correct to three significant figures. Keep full calculator precision during intermediate steps and round only the final answer. On Paper 1, practise rearranging geometric equations and handling powers without relying on automated sequence functions.

A focused correction plan

Use the RevisionDojo sequences and series topic pages to alternate between short drills and mixed applications. After each set, calculate an error rate by category rather than recording only your score.

A useful cycle is:

Day 1: Review one worked video and summarize its decision process.
Day 2: Complete five questions on the same subtopic.
Day 4: Reattempt every incorrect question from a blank page.
Day 7: Complete a mixed set without being told whether each problem is arithmetic or geometric.

Mixed practice matters because an examination question rarely announces the formula you should use. Your first task is usually to recognize the structure.

Conclusion

The main sequences and series errors are incorrect classification, confusion between terms and sums, off-by-one indexing, unjustified use of S∞, sigma-limit mistakes, and weak interpretation of contextual answers. Fixing them requires more than memorizing formulas: you must identify the model, state the target, preserve exact values, and check that the answer makes sense.

RevisionDojo’s per-question Questionbank explanations and worked video solutions are most useful when you pause, predict each step, and reattempt the problem independently. Start with the arithmetic and geometric topic banks, then use Jojo AI and mixed exam-style practice to test whether the correction has become automatic.

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