Answers to Practice with Patterns

1. 5, 8, 11, 14, 17 , 20

Add 3 to the previous term to get the next term.

2. 3, 6, 9, 12, 15 , 18

Add 3 to the previous term to get the next term.

3. 5, 10 , 15, 20, 25, 30

Multiples of five.

4. 40, 20, 16, 8, 4, 2, -2

Take 1/2 of the first term; then subtract 4 from the second term; then take 1/2 of the third term; then subtract 4 from the fourth term; etc.

5. 1, 5, 20, 24, 96, 100, 400, 404, 1616

Add 4, then multiply by 4; add 4; then multiply by 4; etc.

6. 6, 7, 2, 5, 0 5, 0, 7, 2

Add 1, subtract 5, add 3, subtract 5, add 5, subtract 5, ...

7. 12, 14, 10, 16, 8, 18, 6, 20, 4

Add 2, subtract 4, add 6, subtract 8, add 10, subtract 12, ...

8. F, S, T, F, F, S, S, E

The first letter of First, Second, Third, Fourth, Fifth, Sixth, Seventh, Eighth, ...

9. 0, 1, 10, 2, 100, 11, 1000, 3, 20, 101, 10000, 12, 100000, 1001, 110, 4, 1000000, 21, 10000000, 102 1010

It is a sequence of exponents of the numbers 1, 2, 3, 4, 5, 6, ... when written as products of powers of primes ...

1 = 2⁰	0
2 = 2¹	1
3 = 3¹ 2⁰	10
4 = 2²	2
5 = 5¹ 3⁰ 2⁰	100
6 = 3¹ 2¹	11
7 = 7¹ 5⁰ 3⁰ 2⁰	1000
8 = 2³	3
9 = 3² 2⁰	20
10 = 5¹ 3⁰ 2¹	101
11 = 11¹ 7⁰ 5⁰ 3⁰ 2⁰	10000
12 = 3¹ 2²	12
13 = 13¹ 11⁰ 7⁰ 5⁰ 3⁰ 2⁰	100000
14 = 7¹ 5⁰ 3⁰ 2¹	1001
15 5¹ 3¹ 2⁰	110
16 2⁴	4
17 = 17¹ = 13⁰ 11⁰ 7⁰ 5⁰ 3⁰ 2⁰	1000000
18 3² 2¹	21
19 = 19¹ = 17⁰ = 13⁰ 11⁰ 7⁰ 5⁰ 3⁰ 2⁰	10000000
20 = 5¹⁰ 3⁰ 2²	102
21 = 7¹ 5⁰ 3¹ 2⁰	1010

10. (1, 2), (9, 10), (14, 15)

The second number in the ordered pair is 1 more than the first number.

11. (16, 8), (32, 24), (20, 12)

The second number in the ordered pair is 8 less than the first number.

12. (16, 8), (32, 16), (42, 21)

The second number in the ordered pair is 1/2 of the first number.

13. (4, 6, 24), (5, 7, 35), (7, 9, 63)

The third number in the ordered triple is the product of the first 2 numbers.

14. e, f, e, f, c, d, g, h, g, h, c, d, i, j, i

efef cd ghgh cd ijij cd klkl cd mnmn cd ...

15. a, b, c, x, y, z, d, e, f, x, y, z, g, h, i, x

abc xyz def xyz ghi xyz jkl xyz mno xyz pqr xyz ...

16. a, c, e, g, i, k, m, o

Every other letter (1st, 3rd, 5th, 7th, 9th, ...)

17. a, b, b, c, c, c, d, d, d, d, e, e, e, e, e

a bb ccc dddd eeeee ffffff ggggggg hhhhhhhh

18. a, x, b, y, c, z, a, x, b, y, c, z, a, x, b, y

There are two sequences at work here.
Beginning with the first term, every other term is a, b, c, a, b, c, a, b, c, ...
Beginning with the second term, every other term is x, y, z, x, y, z, x, y, z, ...

19. g, a, f, a, e, a, d, a, c, a, b

There are two sequences at work here.
Beginning with the first term, every other term is in descending alphabetical order starting with g: g, f, e, d, c, b, ...
Each even term is the letter a.

20. a, b, c, a, c, d, a, d, e, a, e

abc acd ade aef afg agh ahi aij ajk ...

21. a, b, c, d, e, a, b, c, d, a, b, c, a

abcde abcd abc ab a

22. g, h, j, k, m, n, p, q, s, t, v, w, y

gh jk mn pq st vw yz (2 letters then skip a letter)

23. a, b, c, c, b, a, d, e, f, f, e, d, g, h, i, i

abc cba def fed ghi ihg jkl lkj mno onm pqr rqp ... (3 letters then mirror image)

24. a, c, f, h, k, m, p, r, u

Skips 1 letter, then skips 2 letters, then skips 1 letter, then skips 2 letters ...

25. a, b, a, c, d, c, e, f, e, g, h, g, i, j, i

aba cdc efe ghg iji klk mnm ...

26. a, b, c, a, b, c, d, a, b, c, d, e, a

abc abcd abcde abcdef abcdefg abcdefgh

27. a, a, b, a, b, c, c, d, c, d, e, e, f, e

aabab ccdcd eefef gghgh iijij ...

28. a, b, c, a, d, e, f, d, g, h, i, g, j, k, l, j

abc a def d ghi g jkl j mno m pqr p stu s ...

29. O, T, T, F, F, S, S, E , N , T

First letter of the counting numbers: One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, ...

30. S, M, T, W, T, F , S

First letter of the days of the week

31. 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3

Number of syllables in the months of the year: January, February, March, April, May, June, July, ...

32. 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6

Number of letters in each of the counting numbers: One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, Twelve