Topic 1.2Math AI SL SL16 flashcards

Sequences and sigma notation

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1.2.1

Question

Arithmetic sequence?

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All Flashcards in Topic 1.2

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1.2.14 cards

Card 1definition

Question

Arithmetic sequence?

Answer

A sequence with the same difference each time.

💡 Hint

Same difference.

Card 2concept

Question

Common difference?

Answer

Subtract one term from the next term.

💡 Hint

Next minus previous.

Card 3formula

Question

nth term formula?

Answer

uₙ = u₁ + (n − 1)d

💡 Hint

u₁, d, n.

Card 4concept

Question

8th term of 2, 6, 10, 14, ...?

Answer

💡 Hint

d = 4.

1.2.23 cards

Card 5definition

Question

Sequence or series?

Answer

Sequence = list. Series = sum.

💡 Hint

Commas vs plus signs.

Card 6formula

Question

Sum formula?

Answer

Sₙ = (n/2) × (2u₁ + (n − 1)d)

💡 Hint

For totals.

Card 7concept

Question

Σ from n = 1 to 4 of 2n?

Answer

2 + 4 + 6 + 8 = 20

💡 Hint

Substitute values of n.

1.2.31 cards

Card 8definition

Question

What does sigma mean?

Answer

It is a short way to write a sum.

💡 Hint

Add the terms.

1.2.48 cards

Card 9concept

Question

Simple interest pattern?

Answer

Simple interest adds the same amount each time.

💡 Hint

Equal increase.

Card 10concept

Question

IB gives you two middle terms. How do you find d?

Answer

Write uₙ = u₁ + (n−1)d for each term. Subtract one equation from the other — u₁ cancels, leaving d.

💡 Hint

Label the equations (1) and (2) before subtracting.

Card 11concept

Question

One value or total?

Answer

One value -> nth term. Total -> sum formula.

💡 Hint

Choose the right formula.

Card 12concept

Question

Approximate arithmetic model?

Answer

Real data can be close to arithmetic without being exact.

💡 Hint

Close pattern.

Card 13concept

Question

Why do we subtract the two equations?

Answer

Both equations contain u₁. Subtracting cancels u₁ so only d remains.

💡 Hint

Think: what do both equations have in common?

Card 14concept

Question

If values rise by 60 each step, arithmetic?

Answer

Yes, because the common difference is 60.

💡 Hint

Same increase.

Card 15concept

Question

You solve uₙ > threshold and get n > 11.6. What is n?

Answer

n = 12. Always round up — you need the first whole term that passes the threshold.

💡 Hint

n must be a whole number. Never round down for threshold questions.

Card 16example

Question

Year 3 salary = $31 200. Year 8 salary = $43 200. What is d?

Answer

d = $2 400. Eq(1): u₁ + 7d = 43 200. Eq(2): u₁ + 2d = 31 200. Subtract: 5d = 12 000.

💡 Hint

Subtract the lower-n equation from the higher-n equation.

Topic 1.2 study notes

Full notes & explanations for Sequences and sigma notation

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