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Beskuif die kwadratiese getalpatroon: -145; -122; -101; .. - NSC Mathematics - Question 3 - 2021 - Paper 1
Question 3
Beskuif die kwadratiese getalpatroon: -145; -122; -101; ... 3.1 Skryf die waarde van T₄ neer. 3.2 Toon dat die algemene term van hierdie getalpatroon Tₙ = -n² + 26... show full transcript
Worked Solution & Example Answer:Beskuif die kwadratiese getalpatroon: -145; -122; -101; .. - NSC Mathematics - Question 3 - 2021 - Paper 1
Step 1
Step 2
Toon dat die algemene term van hierdie getalpatroon Tₙ = -n² + 26n - 170 is.
Answer
To show that the general term is valid, we calculate based on the pattern:
- The first term T₁ = -145 can be represented as: a = -145, b = 26, c = -170.
- Using the general term Tₙ = an² + bn + c: We find: a = -1, b = 26, c = -170 leading to Tₙ = -n² + 26n - 170.
Step 3
Tussen watTE TWEWE terme van hierdie kwadratiese getalpatroon sal daar 'n verskil van -121 wees?
Answer
To find between which two terms this difference occurs, set up the equation: Tₘ - Tₙ = -121. Substituting the general term: (-m² + 26m - 170) - (-n² + 26n - 170) = -121. This simplifies to: 2n - 2m = 121, which results in: n = 73, thus between T₃ and T₄.
Step 4
Watter waarde moet by elke term in die getalpatroon gevegt word sodan die waarde van die grootste term in die nuwe kwadratiese getalpatroon wat gevorm word, 1 sal wees?
Answer
Let x be the value added to each term. Using T'ₙ = Tₙ + x: To find when the largest term becomes 1, set: -(-n² + 26n - 170) + x = 1. Solving gives: We find x should be equal to 13, so the equation becomes: T₃ + 2 = 1 yields: T₃ = -1 giving the steady increase required.