Arithmetic applications
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Question
Simple interest pattern?
Answer
Simple interest adds the same amount each time.
š” Hint
Equal increase.
Question
One value or total?
Answer
One value -> nth term. Total -> sum formula.
š” Hint
Choose the right formula.
Question
IB gives you two middle terms. How do you find d?
Answer
Write uā = uā + (nā1)d for each term. Subtract one equation from the other ā uā cancels, leaving d.
š” Hint
Label the equations (1) and (2) before subtracting.
Question
Approximate arithmetic model?
Answer
Real data can be close to arithmetic without being exact.
š” Hint
Close pattern.
Question
Why do we subtract the two equations?
Answer
Both equations contain uā. Subtracting cancels uā so only d remains.
š” Hint
Think: what do both equations have in common?
Question
You solve uā > threshold and get n > 11.6. What is n?
Answer
n = 12. Always round up ā you need the first whole term that passes the threshold.
š” 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.
š” Hint
Same increase.
Question
Year 3 salary = $31 200. Year 8 salary = $43 200. What is d?
Answer
d = $2 400. Eq(1): uā + 7d = 43 200. Eq(2): uā + 2d = 31 200. Subtract: 5d = 12 000.
š” Hint
Subtract the lower-n equation from the higher-n equation.
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