Stage 8 - Q1 - 2 marks
Find the nth term of this linear sequence.
Hint
Compare the terms with 3, 6, 9, ... .
Stage 8 - Q2 - 2 marks
Find the nth term of this linear sequence.
Hint
The constant adjusts \(5n\) to match the first term.
Stage 8 - Q3 - 2 marks
Find the nth term of this linear sequence.
Hint
A decreasing linear sequence needs a negative coefficient.
Stage 8 - Q4 - 2 marks
Find the nth term of this linear sequence.
Hint
Keep the fractional difference exact.
Stage 8 - Q5 - 2 marks
Find term 18 of \(T_{n}=7n-4\).
Hint
The term number is an input, not the value of the term.
Stage 8 - Q6 - 2 marks
A linear sequence has first term \(-5\) and difference 4. Find its nth term.
Hint
Match the formula to the first position.
Stage 8 - Q7 - 3 marks
A linear sequence has \(T_{2}=9\) and \(T_{6}=23\). Find the nth term.
Hint
Divide by the number of steps between the known positions.
Stage 8 - Q8 - 3 marks
Two rules \(3\left(n+2\right)-5\) and \(3n+1\) are proposed. Prove that they give the same term at every position.
Hint
Expand and collect constants rather than testing only a few terms.
Stage 8 - Q9 - 4 marks
A linear sequence has \(T_{5}=31\) and \(T_{11}=67\). Find \(T_{1}\) and \(T_{20}\).
Hint
Use the gap in position numbers to find the repeated difference.
Stage 8 - Q10 - 5 marks
Challenge: a linear sequence has \(T_{4}=17\) and \(T_{9}=37\). Find its nth term, then the first term greater than 100. Justify that your position is the first.
Hint
Find the formula from two positions, then test the threshold with integers.