Algebra and equations · Ages 9–10

The nth term worksheet

Part of: Patterns and rules

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Algebra and equations · Ages 9–10

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

9.The rule is “multiply the position number by 3, then subtract 2”. The 7th number is 23.
True or false?
Answer:
10.9, 16, 23, 30, … Which expression gives the nth number?
- A. 7 × n
- B. 7 × n + 2
- C. n + 7
- D. 9 × n
Choose the right answer
Answer:
11.The rule is “multiply the position number by 6, then subtract 1”. The 15th number is 91.
True or false?
Answer:
12.12, 15, 18, 21, … Which expression gives the nth number?
- A. n + 3
- B. 3 × n + 9
- C. 3 × n
- D. 12 × n
Choose the right answer
Answer:

13.A row of triangles is made from lolly sticks: pattern n uses 2 × n + 1 sticks. Ka-yan uses exactly 21 sticks. Which pattern is it?
Working:
Answer:
14.On this side of a street, the house numbers from the end are 5, 7, 9, 11, … What is the number of the 16th house from the end?
Working:
Answer:
15.Tables are pushed together in a row: n tables seat 2 × n + 2 people. What is the fewest tables that seat all 34 people?
Working:
Answer:
16.On this side of a street, the house numbers from the end are 1, 5, 9, 13, … What is the number of the 40th house from the end?
Working:
Answer:
17.Tables are pushed together in a row: n tables seat 4 × n + 2 people. What is the fewest tables that seat all 42 people?
Working:
Answer:
18.A row of triangles is made from lolly sticks: pattern n uses 2 × n + 1 sticks. May uses exactly 35 sticks. Which pattern is it?
Working:
Answer:

Show the answers and working

The nth term worksheet: Answers and working

1. 18
Put 2 in for n, then work it out.
Put 2 in for n: 9 × 2 = 18, so the 2nd number is 18.
2. 101
Put 11 in for n and work out 9 × 11 first.
Put 11 in for n: 9 × 11 + 2 = 99 + 2 = 101.
3. 30
Put 5 in for n, then work it out.
Put 5 in for n: 6 × 5 = 30, so the 5th number is 30.
4. 91
Find what is added each time, write the nth term as an expression, then put 28 in for n.
It adds 3 each time, so the nth is 3 × n + 7: 3 × 28 + 7 = 91.
5. 3, 3
What is the gap between neighbours? That is what n is multiplied by. Then use the 1st number, 6, to find what is added.
It adds 3 each time, so 3 × n; 3 × 1 = 3 needs 3 more to make 6: 3 × n + 3.
6. 7, 8
What is the gap between neighbours? That is what n is multiplied by. Then use the 1st number, 15, to find what is added.
It adds 7 each time, so 7 × n; 7 × 1 = 7 needs 8 more to make 15: 7 × n + 8.
7. 9
Work backwards: 54 came from × 5 then + 9, so undo the + 9 first.
Work backwards: 54 − 9 = 45, 45 ÷ 5 = 9: the 9th.
8. 10
Work backwards: 63 came from × 6 then + 3, so undo the + 3 first.
Work backwards: 63 − 3 = 60, 60 ÷ 6 = 10: the 10th.

9. False
Follow the rule in order, multiply first and subtract after: start with 7 × 3, then compare with 23.
The 7th: first 7 × 3 = 21, then subtract 2: 19.
10. B. 7 × n + 2
What is added each time? Compare with that number's multiples and see how far off the 1st number, 9, is.
It adds 7 each time, so compare with 7 × n: 7 × 1 = 7, and 2 more makes 9. So the nth is 7 × n + 2.
11. False
Follow the rule in order, multiply first and subtract after: start with 15 × 6, then compare with 91.
The 15th: first 15 × 6 = 90, then subtract 1: 89.
12. B. 3 × n + 9
What is added each time? Compare with that number's multiples and see how far off the 1st number, 12, is.
It adds 3 each time, so compare with 3 × n: 3 × 1 = 3, and 9 more makes 12. So the nth is 3 × n + 9.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 10
Work backwards: 21 came from × 2 then + 1, so subtract the 1 first.
Work backwards: 21 − 1 = 20, 20 ÷ 2 = 10: pattern 10.
14. 35
How much does each house number go up by? How many steps after the 1st house is the 16th?
Each house adds 2. The 16th is 15 steps after the 1st: 5 + 15 × 2 = 35.
15. 16 tables
Try a number of tables n, work out 2 × n + 2 and see if it seats 34; then adjust.
16 tables seat 2 × 16 + 2 = 34, enough for 34; one fewer isn't.
16. 157
How much does each house number go up by? How many steps after the 1st house is the 40th?
Each house adds 4. The 40th is 39 steps after the 1st: 1 + 39 × 4 = 157.
17. 10 tables
Try a number of tables n, work out 4 × n + 2 and see if it seats 42; then adjust.
10 tables seat 4 × 10 + 2 = 42, enough for 42; one fewer isn't.
18. 17
Work backwards: 35 came from × 2 then + 1, so subtract the 1 first.
Work backwards: 35 − 1 = 34, 34 ÷ 2 = 17: pattern 17.

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