Stage 8 - Q1 - 2 marks
Write the first four terms. Multiply by \(2\), then add \(3\).
Hint
Apply both operations to each preceding term.
Stage 8 - Q2 - 2 marks
Write the first four terms. Multiply by \(\frac{1}{2}\), then add \(1\).
Hint
Divide by two before adding one.
Stage 8 - Q3 - 2 marks
Write the first four terms. Multiply by \(3\), then add \(4\).
Hint
Keep the signs when multiplying negative terms.
Stage 8 - Q4 - 2 marks
A rule is add 4 then multiply by 2. The next term is 26. Find the preceding term.
Hint
Reverse the order as well as the operations.
Stage 8 - Q5 - 2 marks
Starting at 6, compare the next term for “subtract 2 then multiply by 3” and “multiply by 3 then subtract 2”.
Hint
Write one rule with brackets.
Stage 8 - Q6 - 2 marks
The rule is multiply by 3 then subtract 8. Find a starting term that remains unchanged.
Hint
An unchanged sequence has the same input and output.
Stage 8 - Q7 - 3 marks
The rule is add 2 then multiply by 2. Term 5 is 124. Find term 2.
Hint
Count the three steps from position 2 to position 5.
Stage 8 - Q8 - 4 marks
The first term is 3. The rule is add 9 then divide by 2. Explain why every term stays below 9.
Hint
Rewrite “add 9 then divide by 2” as an average.
Stage 8 - Q9 - 4 marks
The rule is “multiply by \(-1\) then add 12”. Which starting value gives a constant sequence? What happens to any other starting value?
Hint
Apply the rule twice before testing a special starting value.
Stage 8 - Q10 - 5 marks
Challenge: a sequence uses “multiply by 2 then subtract 3”. Its fifth term is 99. Find its first term, then explain why no later term can equal 3.
Hint
Reverse the operations, then compare each term with the fixed value 3.