Free Printable Sequences and Series Review

1.

Given the recursive formula, find the explicit form
a_n = a_n-1 + 5
a₁ = -16

a)

a_n = 5 + (n-1)(-16)

b)

a_n = -11 + (n-1)(5)

c)

a_n = 16 + (n-1)(5)

d)

a_n = -16 + (n-1)(5)

2.

Write a recursive rule for the sequence a_n = 17 + (n-1)(-16)

a)

a₁ = 17
a_n = a_n-1 + 16

b)

a₁ = 17
a_n = a_n-1 - 17

c)

a₁ = 17
a_n = a_n-1 - 15

d)

a₁ = 17
a_n = a_n-1 - 16

3.

The cell phone story sells 100 phones in January, 110 phones in February, and 120 phones in March. This pattern continues. What is the explicit rule for this pattern?

a)

$a_n=100n\ +\ 10$

b)

$a_n=100\ +10\left(n-1\right)$

c)

$a_n=a_{\left(n-1\right)}+10$

d)

$a_n=a_{\left(n-1\right)}+100$

4.

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

a)

a_n= 10n + 17

b)

a_n = 7n - 17

c)

a_n = -7n + 17

d)

a_n = 7n + 3

5.

A website starts with 120 users. The expect to gain 20% every year. What is the explicit rule for this growth?

a)

$a_n=120\left(20\right)^{\left(n-1\right)}$

b)

$a_n=20\left(120\right)^{\left(n-1\right)}$

c)

$a_n=120\left(1.20\right)^{\left(n-1\right)}$

d)

$a_n=120\left(0.20\right)^{\left(n-1\right)}$

6.

The explicit rule for a sequence is: $a_n=10\left(-2\right)^{\left(n-1\right)}$ What is the recursive rule for the sequence?

a)

$a_1=-2,\ \ a_n=-2\left(10\right)^{\left(n-1\right)}$

b)

$a_1=10,\ a_n=10\left(a_{\left(n-1\right)}\right)^{ }$

c)

$a_1=-2,\ a_n=10\left(a_{\left(n-1\right)}\right)^{ }$

d)

$a_1=10,\ a_n=-2\left(a_{\left(n-1\right)}\right)$

7.

A student group starts walking for exercise. They start by walking 1 mile. They increase the distance they walk by 0.1 miles every day. If they do this for a 31 day month how far will they walk?

a)

62 miles

b)

77.5 miles

c)

80 miles

d)

100 miles

8.

A lemonade stand starts 10 weeks before the end of the summer. It makes $8 the first week, $11 the second week, $14 the third week, and so on. How much will it make for the whole summer?

a)

$80

b)

$160

c)

$215

d)

$340

9.

The first day a Instagram video is out it gets 20 views. The number of views triples every day for the rest of the week. How many views does the video get?

a)

10,430

b)

12,750

c)

17,990

d)

21860

10.

A YouTube channel makes $50 the first week. The amount goes up 5% a week for 6 weeks. How much money will come in from the channel? (Round to the nearest penny.)

a)

$300.05

b)

$320.15

c)

$340.10

d)

$370.75

11.

What is $\sum_{k=1}^5\left(5k+2\right)$ equal to?

a)

25

b)

45

c)

65

d)

85

12.

What is $\sum_{n=1}^4\left[7\left(-2\right)^{\left(n-1\right)}\right]$

a)

28

b)

-28

c)

-35

d)

35

Sequences and Series Review

Total questions: 12

Worksheet time: 3hrs 0mins

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