Mathematics 8: Sequences

Flashcards covering key definitions, sequence generation rules, worksheet problems, and nth-term formulas for arithmetic and geometric sequences.

What is a sequence?

A list of numbers which follow a pattern.

What is a term in a sequence?

Each number on the sequence is called a term.

What do ellipses located at the end of a sequence indicate?

Ellipses located at the end of a sequence indicate that there are many terms that follow.

What sequence of $10$ terms is generated by starting at $3$ and adding $5$?

$$3, 8, 13, 18, 23, 28, 33, 38, 43, 48$$

What sequence of $10$ terms is generated by starting at $100$ and subtracting $10$?

$$100, 90, 80, 70, 60, 50, 40, 30, 20, 10$$

What are the first $10$ multiples of $6$?

$$6, 12, 18, 24, 30, 36, 42, 48, 54, 60$$

What are ten multiples of $6$ starting at $18$?

$$18, 24, 30, 36, 42, 48, 54, 60, 66, 72$$

What are ten multiples of $7$ starting at $21$?

$$21, 28, 35, 42, 49, 56, 63, 70, 77, 84$$

What sequence is generated using $5n - 2$ for $n = 1, 2, 3, 4, 5, 6$?

$$3, 8, 13, 18, 23, 28$$

What sequence is generated using $3n + 1$ for $n = 1, 2, 3, 4 \times 10$?

$$4, 7, 10, 13, 16, 19, 22, 25, 28, 31$$

What sequence is generated starting at $15$ and adding $1, 2, 3, 4, 5$ successively?

$$15, 16, 18, 21, 25, 30$$

What are the first $6$ powers of $2$?

$$2, 4, 8, 16, 32, 64$$

What are the first $6$ powers of $\frac{1}{2}$?

$$\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \frac{1}{64}$$

What are the first $5$ terms of an arithmetic sequence with $t_1 = 4$ and $d = 3$?

$$4, 7, 10, 13, 16$$

What are the first $5$ terms of a geometric sequence with $t_1 = 4$ and $r = 3$?

$$4, 12, 36, 108, 324$$

Worksheet No. 1 (Q1): What sequence of $10$ terms is generated by starting at $-1$ and adding $3$?

$$-1, 2, 5, 8, 11, 14, 17, 20, 23, 26$$

Worksheet No. 1 (Q2): What sequence of $10$ terms is generated by starting at $20$ and subtracting $6$?

$$20, 14, 8, 2, -4, -10, -16, -22, -28, -34$$

Worksheet No. 1 (Q3): What are the first ten multiples of $12$?

$$12, 24, 36, 48, 60, 72, 84, 96, 108, 120$$

Worksheet No. 1 (Q4): What are ten multiples of $9$ starting at $27$?

$$27, 36, 45, 54, 63, 72, 81, 90, 99, 108$$

Worksheet No. 1 (Q5): What sequence is generated using $n = 1, 2, 3, 4, 5, 6$ for $7n - 2$?

$$5, 12, 19, 26, 33, 40$$

Worksheet No. 1 (Q6): What sequence is generated starting at $2$ and adding $2, 4, 8, 16, 32$ successively?

$$2, 4, 8, 16, 32, 64$$

Worksheet No. 1 (Q7): What are the first $6$ powers of $3$?

$$3, 9, 27, 81, 243, 729$$

Worksheet No. 1 (Q8): What are the first $6$ powers of $\frac{1}{4}$?

$$\frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \frac{1}{1024}, \frac{1}{4096}$$

Worksheet No. 1 (Q9): What are the first $5$ terms of an arithmetic sequence with $t_1 = 9$ and $d = 8$?

$$9, 17, 25, 33, 41$$

Worksheet No. 1 (Q10): What are the first $5$ terms of a geometric sequence with $t_1 = 5$ and $r = 3$?

$$5, 15, 45, 135, 405$$

What is the formula for finding the nth term of an arithmetic sequence?

$$t_n = t_1 + (n - 1)d$$

In the arithmetic sequence $10, 6, 2, -2, -6, -10, \dots$, what is $t_{60}$?

$$-226$$

In the arithmetic sequence $7, 12, 17, 22, 27, 32, \dots$, what is $t_{45}$?

$$227$$

In the arithmetic sequence $-7, -1, 5, 11, 17, 23, \dots$, what is $t_{35}$?

$$197$$

What is the formula for finding the nth term of a geometric sequence?

$$t_n = t_1(r)^{n - 1}$$

In the geometric sequence $2, 6, 18, 54, \dots$, what is $t_{10}$?

$$39\,366$$

In the geometric sequence $2, 4, 8, 16, 32, \dots$, what is $t_{15}$?

$$32\,768$$