Purpose: Verify pattern-recognition and arithmetic prerequisite skills before tackling sequences and series formulas.
Prerequisite Skills
Question 1 [2 marks]
Find the next two terms of the pattern \( 3, 7, 11, 15, \ldots \). Identify the rule.
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Question 2 [2 marks]
Find the next two terms of \( 2, 6, 18, 54, \ldots \). Identify the rule.
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Question 3 [3 marks]
Solve the linear equation \( 5n - 3 = 47 \) for \( n \).
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Question 4 [3 marks]
Evaluate \( \dfrac{10}{2}(2 \cdot 5 + 9 \cdot 3) \).
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Question 5 [3 marks]
Compute \( 2^7 - 1 \) and \( \dfrac{2^7 - 1}{2 - 1} \). Why are they equal?
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Question 6 [3 marks]
For the function \( f(n) = 3n + 1 \), evaluate \( f(1), f(2), f(3), f(10) \). What pattern do the outputs form?
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Reflection
Question 7 [Reflection]
When you see the formula \( t_n = a + (n - 1)d \), do you understand each piece (\( a, n, d \))? Be honest about which symbol confuses you.
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