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All 8 Flashcards — Arithmetic applications
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Question
Simple interest pattern?
Answer
Simple interest adds the same amount each time.
💡 Hint
Equal increase.
Question
One value or total?
Answer
One value -> nth term. Total -> sum formula.
💡 Hint
Choose the right formula.
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.
Question
Approximate arithmetic model?
Answer
Real data can be close to arithmetic without being exact.
💡 Hint
Close pattern.
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?
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.
Question
If values rise by 60 each step, arithmetic?
Answer
Yes, because the common difference is 60.
💡 Hint
Same increase.
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.
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