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Flip to reveal answersHow do you spot an arithmetic model in a word problem?
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All 9 Flashcards — Applications
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Question
How do you spot an arithmetic model in a word problem?
Answer
Look for a quantity that changes by the same amount each step (a fixed raise, a fixed number per row). Then u₁ = the start and d = the constant change.
Question
How do you translate 'starts at 20, rises by 4 each time'?
Answer
u₁ = 20 and d = 4. The nth value is uₙ = 20 + (n − 1)4.
Question
In a decreasing arithmetic sequence, when is the sum Sₙ greatest?
Answer
At the last term that is still positive or zero — find where uₙ = 0. Adding later negative terms only shrinks the total.
Question
How do you find the maximum sum of an arithmetic sequence?
Answer
Solve uₙ = 0 for n, then evaluate Sₙ at that position. Example: u₁ = 48, d = −3 ⇒ u₁₇ = 0 ⇒ S₁₇ = 408.
Question
How can the GDC help find a maximum sum (Paper 2)?
Answer
Graph Sₙ or scan a table of Sₙ and read off the largest value; the peak is at the term where uₙ = 0.
Question
How do you find the first term past a threshold?
Answer
Set up an inequality with uₙ, solve for n, then round to the next whole number (n must be a positive integer).
Question
A sequence has u₁ = 90, d = −7. Which is the first term below 20?
Answer
90 − 7(n − 1) < 20 ⇒ n > 11 ⇒ n = 12; u₁₂ = 13.
Question
Does 'total' mean uₙ or Sₙ?
Answer
A total or 'altogether' is a sum, so use Sₙ. A single 'nth' value is a term uₙ.
Question
Why must n be a whole number in application problems?
Answer
n counts terms (rows, years, balls), which only come in whole numbers; round a decimal n to the appropriate integer and check.
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Full study notes for Applications
Topic 1.2 hub
Arithmetic sequences & series
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Math AA SL exam skills
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