Math worksheet on sequences and nth terms with exercises for finding terms, rules, and solving equations.

1. a. 3, 5, 7, 9, 11, 13
b. 5, 10, 15, 20, 25, 30
c. 0, 2, 4, 6, 8, 10
d. 7, 10, 13, 16, 19, 22
e. 2, 5, 8, 11, 14, 17
f. 1, 5, 9, 13, 17, 21
g. 7, 9, 11, 13, 15, 17
h. 5, 8, 11, 14, 17, 20
i. -2, -1, 0, 1, 2, 3
j. -2, 1, 4, 7, 10, 13
k. 9, 8, 7, 6, 5, 4
l. 17, 14, 11, 8, 5, 2
m. 28, 26, 24, 22, 20, 18
n. 2, 6, 12, 20, 30, 42
o. 0, 3, 8, 15, 24, 35
p. 1, 4, 9, 16, 25, 36
q. 2, 8, 18, 32, 50, 72
r. 4, 16, 36, 64, 100, 144
s. 1, 1/2, 1/3, 1/4, 1/5, 1/6
t. 1/3, 2/5, 3/7, 4/9, 5/11, 6/13
u. 1/5, 3/8, 5/11, 7/14, 9/17, 11/20

2. a. Term 10 = 21, Term 50 = 101
b. Term 10 = 50, Term 50 = 250
c. Term 10 = 18, Term 50 = 98
d. Term 10 = 34, Term 50 = 154
e. Term 10 = 29, Term 50 = 149
f. Term 10 = 37, Term 50 = 197
g. Term 10 = 25, Term 50 = 105
h. Term 10 = 32, Term 50 = 152
i. Term 10 = 7, Term 50 = 47
j. Term 10 = 25, Term 50 = 145
k. Term 10 = 0, Term 50 = -40
l. Term 10 = -10, Term 50 = -130
m. Term 10 = 10, Term 50 = -70
n. Term 10 = 110, Term 50 = 2550
o. Term 10 = 99, Term 50 = 2499
p. Term 10 = 100, Term 50 = 2500
q. Term 10 = 200, Term 50 = 5000
r. Term 10 = 400, Term 50 = 10000
s. Term 10 = 1/10, Term 50 = 1/50
t. Term 10 = 10/21, Term 50 = 50/101
u. Term 10 = 19/32, Term 50 = 99/152

3. a. nth term: 2n - 1, Term 20 = 39
b. nth term: 3n, Term 20 = 60
c. nth term: 3n - 2, Term 20 = 58
d. nth term: 4n + 3, Term 20 = 83
e. nth term: 3n + 1, Term 20 = 61
f. nth term: 10n - 6, Term 20 = 194
g. nth term: 2n + 15, Term 20 = 55
h. nth term: 4n - 2, Term 20 = 78
i. nth term: 2n + 6, Term 20 = 46
j. nth term: n + 2, Term 20 = 22
k. nth term: 3n - 7, Term 20 = 53
l. nth term: -2n + 22, Term 20 = -18
m. nth term: -3n + 10, Term 20 = -50
n. nth term: -4n + 29, Term 20 = -51
o. nth term: n/(3n-1), Term 20 = 20/59
p. nth term: 2n/(3n+1), Term 20 = 40/61

4. a. First term = 9
b. First term = 12
c. First term = 7
d. First term = 4

5. a. Term 25
b. Term 18
c. Term 21

6. a. Yes
b. Yes
c. Yes
d. No
e. 18