Stage 8 - Q1 - 2 marks
Is the given value a term? Justify.
Hint
Solve \(4n+3=31\).
Stage 8 - Q2 - 2 marks
Is the given value a term? Justify.
Hint
A valid position must be a positive integer.
Stage 8 - Q3 - 2 marks
Is the given value a term? Justify.
Hint
Move the constant before dividing.
Stage 8 - Q4 - 2 marks
Is the given value a term? Justify.
Hint
A decreasing sequence can still contain positive values.
Stage 8 - Q5 - 2 marks
For \(T_{n}=2.5n+1\), find the position of the term 31.
Hint
Treat the fractional coefficient exactly.
Stage 8 - Q6 - 2 marks
Find the first term above 80 in \(T_{n}=7n-3\).
Hint
Check the term immediately before the proposed answer.
Stage 8 - Q7 - 3 marks
How many positive terms are in \(T_{n}=35-4n\)?
Hint
Positive excludes zero.
Stage 8 - Q8 - 3 marks
Explain why 100 cannot occur in \(T_{n}=6n+5\) without listing the terms.
Hint
Check divisibility after removing the constant.
Stage 8 - Q9 - 4 marks
Can a term of \(3n+1\) equal a term of \(3n+7\) at a different position? Give an example and explain why this differs from using the same position.
Hint
Try shifting one position number by two.
Stage 8 - Q10 - 5 marks
Challenge: sequences A and B have rules \(8n+3\) and \(5n+18\). Find the shared position where their values match, then describe which is larger before and after that position.
Hint
Compare the two expressions by subtracting them.