Practice sheet

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

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$a_1 = 3$ and $a_{n+1} = 2a_n - 7$ . Find $a_3$ .
Write a formula for $a_n$ , starting at $n = 1$ : $1,6, 11, 16, \dots$
$a_n = n^2 + 5$ . Complete the table.
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 $n = 1$ : $2, 8, 32, \dots$
How many terms does $\displaystyle\sum_{k=3}^{ 17 } (2k + 1)$ have?
Find $\displaystyle\sum_{k=1}^{ 30 } (3k + 7)$ .
Find $1 + 2 + 3 + \dots + 94$ .
Find the sum of the first 6 terms of the geometric sequence with $a_1 = 8$ and ratio 3.
Find $\displaystyle\sum_{k=0}^{ 6 } 2^k$ .
You put 764 dollars in a savings account at the end of each year, at 5 % interest a year. How much is in the account right after the 12th payment? Round to the nearest cent.

Answers

$-9$
$5 n - 4$
$6, 9, 14, 21$
$98$
$8$
Geometric, with ratio 2
$81$
$4$
$2 \cdot 4^{n - 1}$
$15$
$1605$
$4465$
$2912$
$127$
$\frac{622627054674848431}{51200000000000}$