Practice sheet

Fresh questions from the whole chapter, to do on paper.

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Write $7(x - 3)$ without parentheses. What is the constant term?
Combine like terms in $9x + 6 - 11x + 4$ . What is the coefficient of $x$ ?
Simplify $6x - (5x - 2)$ . What is the constant term?
Solve $3x + 3 = -18$ . $x = \;?$
Solve $4x + 8 = 3x + 9$ . $x = \;?$
Solve $6(x + 4) = 30$ . $x = \;?$
Solve $8x + 5 < 45$ . Give the solution set as an interval.
Solve $-2x + 17 \le 9$ . Give the solution set as an interval.
You have 109 dollars and tickets cost 9 dollars each. Solve $9t \le 109$ : what is the greatest number of tickets you can buy?
An arithmetic sequence has $a_1 = 14$ and common difference 2. Find $a_{ 43 }$ .
In an arithmetic sequence, $a_{ 4 } = 28$ and $a_{ 9 } = 68$ . Find the common difference.
What kind of sequence is $3, 6, 12, 24, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $1, 2, 4, 8, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $3, 12, 48, 192, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $3, 9, 27, 81, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 8, 16, 32, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 8, 32, 128, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $4, 12, 36, 108, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $1, 4, 16, 64, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $5, 20, 80, 320, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $2, 4, 8, 16, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $5, 15, 45, 135, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $5, 10, 20, 40, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 6, 18, 54, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 16, 64, 256, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $1, 3, 9, 27, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
A geometric sequence has $a_1 = 3$ and ratio 3. Find $a_{ 4 }$ .
Find the common ratio of the geometric sequence $8, 32, 128, \dots$
Write a formula for $a_n$ , starting at $n = 1$ : $2, 8, 32, \dots$

Answers

$-21$
$-2$
$2$
$-7$
$1$
$1$
$(-\infty, 5)$
$[4, \infty)$
$12$
$98$
$8$
Geometric, with ratio 2
$81$
$4$
$2 \cdot 4^{n - 1}$