Arithmetic Progressions

What’s inside

Choose the correct answer to unlock each row.

1. What is the common difference in 4, 9, 14, 19, …? (Compare two consecutive terms.)
   4 · 5 · 6 · −5
2. What are the next two terms in 20, 16, 12, 8, …? (The sequence decreases by the same amount each time.)
   0, −4 · 3, −1 · 4, 0 · 4, −1
3. What is the missing term in 3, 8, __, 18, 23? (Find the constant difference between consecutive terms.)
   12 · 13 · 14 · 15
4. Which sequence is an arithmetic progression? (Look for a sequence with a constant difference.)
   1, 4, 9, 16, … · 2, 4, 8, 16, … · 6, 10, 14, 18, … · 10, 8, 5, 1, …
5. What is the nth-term rule for 3, 7, 11, 15, …? (Use the common difference as the coefficient of n.)
   3n + 1 · 4n + 1 · 4n + 3 · 4n − 1
6. What is the nth-term rule for 8, 13, 18, 23, …? (The first term corresponds to n = 1.)
   4n + 4 · 5n + 3 · 5n + 8 · 5n − 3
7. What is the nth-term rule for 15, 11, 7, 3, …? (The common difference is negative.)
   11 − 4n · 15 − 4n · 19 + 4n · 19 − 4n
8. The nth term of a sequence is 6n + 2. What is the 8th term? (Substitute 8 for n.)
   46 · 48 · 50 · 56
9. A progression begins 7, 12, 17, 22, … What is its 20th term? (Use the first term and common difference to find the 20th term.)
   97 · 100 · 102 · 107
10. The nth term is 5n + 4. Which term is 49? (Set the nth-term rule equal to 49 and solve for n.)
    The 8th term · The 9th term · The 10th term · The 11th term
11. Is 46 in the sequence 4, 10, 16, 22, …? (Use the common difference to check whether 46 is a term.)
    No, it is not in the sequence · Yes, it is the 7th term · Yes, it is the 8th term · Yes, it is the 9th term
12. An arithmetic progression has 3rd term 14 and 7th term 30. What is its nth-term rule? (Find the common difference from the change over four steps.)
    3n + 5 · 4n + 2 · 4n + 6 · 5n − 1
13. A theatre has 10 seats in its first row. Each new row has 4 more seats than the previous row. How many seats are in the 12th row? (From row 1 to row 12, there are 11 increases.)
    50 · 52 · 54 · 58
14. Maya saves £6 in week 1 and increases her weekly saving by £2 each week. How much does she save in week 10? (There are nine increases from week 1 to week 10.)
    £20 · £22 · £24 · £26
15. A staircase has 5 tiles in its first step, 8 in its second, and 11 in its third. How many tiles are used in the first 10 steps altogether? (Find the 10th term, then add the first and last terms and multiply by half the number of terms.)
    155 · 170 · 185 · 200