Algebraic expressions · Ages 12–13

Growing patterns and the n-th term worksheet

Part of: Algebraic expressions & sequences

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Algebraic expressions · Ages 12–13

Numsprite
numsprite.com

Name:Date:Score:／48

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

1.The n-th term of a sequence is 12n + 17. Term 18 is .
Answer:
2.The n-th term of a sequence is 8n + 7. Term 16 is .
Answer:
3.The n-th term of a sequence is 11n + 7. 249 is term .
Answer:
4.The n-th term of 2, 4, 6, 8, … can be written an + b: a = , b = .
Fill in each blank
Answer:
5.The n-th term of a sequence is 10n + 11. 191 is term .
Answer:
6.The n-th term of 4, 7, 10, 13, … can be written an + b: a = , b = .
Fill in each blank
Answer:
7.The n-th term of 0, 3, 8, 15, … is n² + b, where b = .
Answer:
8.The n-th term of −8, −5, 0, 7, … is n² + b, where b = .
Answer:

13.Square n has n rows of n players. How many more are needed to go from square 15 to square 16?
Working:
Answer:
14.A club charges $80 for month 1, then $20 a month. n months cost (an + b) dollars: a = , b = ; 11 months cost .
Fill in each blank
Working:
Answer:
15.Matchsticks make a row of little houses. How many matchsticks do 15 houses take?
- A. 81
- B. 76
- C. 90
- D. 75
Choose the right answer
Working:
Answer:
16.Tables join in a row: 5 people on each side of every table, and 1 at each end. n tables seat (n + ); 10 tables seat .
Fill in each blank
Working:
Answer:
17.A hall's row 1 has 18 chairs, and each row after has 9 more. How many chairs are in row n?
- A. 9n + 27
- B. 18n + 9
- C. 9n + 9
- D. 9n + 18
Choose the right answer
Working:
Answer:
18.A path is 42 m long. A tree goes in every 2 m, with one at each end. That makes sections and trees.
Fill in each blank
Working:
Answer:

Show the answers and working

Growing patterns and the n-th term worksheet: Answers and working

1. 233
Put 18 for n: 12 × 18 + 17 = 216 + 17 = 233.
2. 135
Put 16 for n: 8 × 16 + 7 = 128 + 7 = 135.
3. 22
Backwards: 249 − 7 = 242, 242 ÷ 11 = 22.
4. 2, 0
It adds 2 each time, so a = 2. With n = 1, a + b is term 1, 2: b = 2 − 2 = 0.
5. 18
Backwards: 191 − 11 = 180, 180 ÷ 10 = 18.
6. 3, 1
It adds 3 each time, so a = 3. With n = 1, a + b is term 1, 4: b = 4 − 3 = 1.
7. −1
n² gives 1, 4, 9, 16; each term less n² is −1, so b = −1.
8. −9
n² gives 1, 4, 9, 16; each term less n² is −9, so b = −9.

9. D. 53
The dots go 3, 8, 13, adding 5 each time. From pattern 1 to pattern 11 that is 10 additions: 3 + 10 × 5 = 3 + 50 = 53.
10. D. 5n + 1
The sticks go 6, 11, 16, adding 5 each time. Compared with 5n, each is 1 more: 5n + 1.
11. A. 55
The dots go 1, 3, 6, … with the amount added growing by 1: pattern 9 has 45, and pattern 10 adds 10, making 55.
12. D. 91
The dots go 1, 3, 6, … with the amount added growing by 1: pattern 12 has 78, and pattern 13 adds 13, making 91.

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

13. 31
Square 15 has 15² = 225 and square 16 has 16² = 256: 256 − 225 = 31 more.
14. 20, 60, 280
20 more a month, so a = 20; with n = 1, a + b is month 1's 80: b = 80 − 20 = 60. 20 × 11 + 60 = 280.
15. B. 76
6 for the first house, then 5 more each, 14 times: 6 + 70 = 76. Or use 5n + 1.
16. 10, 2, 102
Each table has 5 × 2 at its sides, and there are only 2 at the ends. So 5 × 2 × n + 2. Don't count two ends on every table.
17. C. 9n + 9
18 + (n − 1) × 9 = 9n + 9. With n = 1: 9 + 9 = 18.
18. 21, 22
42 ÷ 2 = 21 sections; there is one more tree than sections: 22.

Numsprite · numsprite.com/en/worksheets/algebraic-expressions-and-sequences/nth-term-of-a-sequence