Name: _________________________
Common Core Algebra 9H – Review Sheet
Date: _________
Aims #85-92
1. Determine if the following sequences are arithmetic or geometric. Then, write the explicit and
recursive formulas.
a. 2, 13, 24, 35, . . .
d. {−9, −1,
−1 −1
, ,…}
9 81
b. 10, -50, 250, -1250, . . .
c. -2x, 3x + 8, 8x + 16, . . .
e. { -3, -7, -11, … }
f. {2, −6, 18, −54, … }
2. Find the first 5 terms of each sequence.
a. an+1 = -8an, a1 = 3
b. f(n + 1) = f(n) – 5, a1 = -2
c. an = 3an-1 + 2, a1 = 4
d. 𝑓(𝑥) = 5𝑥 − 4; 𝑥 ≥ 1
e. 𝐴𝑛 = 6 − 4(𝑛 − 1); 𝑛 ≥ 1
f. 𝐴𝑛 = 4(−2)𝑛−1 ; 𝑛 ≥ 1
3. Determine the common difference or common ratio for each sequence.
100
,...
3
4. For each of the following sequences, find the 100th term.
a. -17, -15.3, -13.6, . . .
b. 12, 20,
c. ab2, 4a3b5, 16a5b8, . . .
a. 5, 15, 45, 135, . . .
b. -17, -13, -9, -5, . . .
c. -1, -3.5, -6, -8.5, . . .
5. For a certain arithmetic sequence, the first term is -51 and d = -5. If an = -96, then what is the
value of n?
6. Write the explicit formula for the sequence 1, 4, 9, 16, . . . Then, find the 21st term.
7. Let 𝑎1 = 55 and 𝑎16 = 85 be part of an arithmetic sequence. Find 𝑎3 .
8. Let 𝑎4 = 20 be part of a geometric sequence and the common ratio be 5. Find 𝑎1 .
9. Let 𝑎5 = −12 be part of a geometric sequence and the common ratio is -1/3. Find the general rule
for the nth term.
10. Find 𝑛 in the arithmetic sequence {−2, 5, 12, 19, … } such that 𝑎(𝑛) = 138.
11. Let 𝑎14 = 5 and 𝑎20 = −35 be part of an arithmetic sequence.
a. Find d.
b. Find a1.
c. Write the general rule for the sequence.
d. Find the 98th term in the sequence.
12. 2n + 5, 5n + 11, 9n + 2 are the first three terms of an arithmetic sequence for some value of n.
a. Find the value of n.
b. What is the 12th term of the sequence?
13. Find the missing values for the arithmetic sequence {11, 𝑎, 𝑏, 𝑐, 47}.
14. Find the values of a, b, c, and d in the arithmetic sequence 16, a, b, c, d, 28.
15. Find all possible missing values for the geometric sequence {2, 𝑎, 𝑏, 𝑐, 32}.
16. Find all possible values of a, b and c in the geometric sequence 1875, a, b, c, 3.
17. Suppose you are given the terms of a geometric sequence a5 = -162 and a6 = -486, find r and a1.
18. Find the rule for the nth term of an arithmetic sequence if a9 = 3 and a26 = -82.
19. Given the arithmetic sequence such that 𝑎15 = 73 and 𝑎70 = 348. Find an explicit rule for the 𝑛𝑡ℎ
term.
20. Two terms of a geometric sequence are a4 = -16 and a6 = -256. Find a rule for the nth term.
21. For each arithmetic sequence, write the sum in sigma notation and then find the sum using the
formula Sn 
n  a1  an 
2
.
a. 2, 6.5, 11, 15.5, 20
b. -1, -4, -7, -10, -13, -16, -19
22. Find the sum of each arithmetic series using the formula Sn 
a. 13 + 19 + 25 + … + 157
n  a1  an 
2
.
b. 22.5 + 21 + 19.5 + … + 3
23. Write the sum in summation notation and then find the sum using the formula Sn 
a1 1  r n 
1 r
.
1
1
1
1
+
+
+
4 16 64 256
24. A certain bacteria has an initial population of 20 bacteria and each hour the population doubles in
a. 2 + 8 + 32 + 128 + 512 + 2048
b. 1 +
size. Write an explicit and recursive formula to represent this situation. Then, determine the
amount of bacteria after 14 hours.
25. Joe’s starting salary at his job was 40,000 per year. Every year he receives a raise of $4,000.
Write an explicit and recursive formula to represent this situation. Then, find his salary after 7
years.
26. John uses his cell phone 12 minutes in a day. Since his new job it has increased every day since by
6 minutes. When will John reach 60 minutes of cell phone use?