Free Printable 09-02 Arithmetic & Geometric Sequences

1.

Write an explicit formula for the sequence

6, 10, 14, 18, ...

a)

$a_n=6+4\left(n-1\right)$

b)

$a_n=2+4\left(n-1\right)$

c)

$a_n=6\left(4\right)^{\left(n-1\right)}$

d)

$a_n=6\left(4\right)\left(n-1\right)$

2.

What is the 100th term in the sequence

6, 10, 14, 18, ...

a)

402

b)

406

c)

598

d)

604

3.

Write an explicit formula for the sequence

-2, 2, -2, 2, -2, 2, ...

a)

$b_n=-2+2\left(n-1\right)$

b)

$b_n=-2\left(-1\right)^{\left(n-1\right)}$

c)

$b_n=-2+4\left(n-1\right)$

d)

$b_n=-1\left(2\right)^{\left(n-1\right)}$

4.

What is the 100th term in the sequence

-2, 2, -2, 2, -2, 2, ...

a)

-2

b)

2

c)

100

d)

-101

5.

Write an explicit formula for the sequence

2, 6, 18, 54, ...

a)

$c_n=2\left(6\right)^{\left(n-1\right)}$

b)

$c_n=2+3\left(n-1\right)$

c)

$c_n=2+6\left(n-1\right)$

d)

$c_n=2\left(3\right)^{\left(n-1\right)}$

6.

What is the 20th term in the sequence

2, 6, 18, 54, ...

a)

2324522934

b)

59

c)

6973568802

d)

3486784403

7.

Write an explicit formula for the sequence

-4, 1, 6, 11, ...

a)

$d_n=-4\left(5\right)^{\left(n-1\right)}$

b)

$d_n=5\left(-4\right)^{\left(n-1\right)}$

c)

$d_n=5-4\left(n-1\right)$

d)

$d_n=-4+5\left(n-1\right)$

8.

What is the 100th term in the sequence

-4, 1, 6, 11, ...

a)

441

b)

491

c)

466

d)

391

9.

Write an explicit formula for the sequence

26, 15, 4, -7, ...

a)

$e_n=26+11\left(n-1\right)$

b)

$e_n=26\left(-11\right)^{\left(n-1\right)}$

c)

$e_n=26-11\left(n-1\right)$

d)

$e_n=11+26\left(n-1\right)$

10.

What is the 100th term in the sequence

26, 15, 4, -7, ...

a)

-1063

b)

1115

c)

-1074

d)

1126

11.

Write an explicit formula for the sequence

3, 6, 12, 24, ...

a)

$f_n=3+2\left(n-1\right)$

b)

$f_n=3\left(2\right)^{\left(n-1\right)}$

c)

$f_n=2\left(3\right)^{\left(n-1\right)}$

d)

$f_n=2\left(3\right)^{\left(n-1\right)}$

12.

What is the 25th term in the sequence

3, 6, 12, 24, ...

a)

53

b)

77

c)

-1694577219

d)

50331648

13.

The fourth and seventh terms of an arithmetic sequence are -8 and 4 respectively. Find an explicit formula for the sequence.

a)

$a_n=-20+4\left(n-1\right)$

b)

$a_n=-8+4\left(n-1\right)$

c)

$a_n=4-8\left(n-1\right)$

d)

$a_n=4-20\left(n-1\right)$

14.

The second and eighth terms of a geometric sequence are 3 and 192 respectively. Find an explicit formula for the sequence.

a)

$g_n=192\left(3\right)^{\left(n-1\right)}$

b)

$g_n=2\left(\frac{3}{2}\right)^{\left(n-1\right)}$

c)

$g_n=\frac{3}{2}\left(2\right)^{\left(n-1\right)}$

d)

$g_n=3\left(192\right)^{\left(n-1\right)}$

15.

The bungy-bungy tree in the Amazon rain forest grows an average of 3.2 cm per week. If it is currently 700 cm tall today, what will be the height at the end of one year (52 week)?

a)

882 cm

b)

863.2 cm

c)

36402.3 cm

d)

35702.3 cm

16.

A patio design is in the shape of a trapezoid consisting of rows of congruent slate tiles. The first row has 15 tiles and the last row has 55 tiles. If each row has 2 more tiles than the previous row, how many rows of tiles are there?

a)

15

b)

19

c)

20

d)

21

17.

Is the sequence below arithmetic, geometric, neither, or both?

5, -4, -13, -22, -31, ...

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

18.

Is the sequence below arithmetic, geometric, neither, or both?

1, 4, 16, 64, 256 ...

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

19.

Is the sequence below arithmetic, geometric, neither, or both?

2, 5, 9, 14, 20, 27, ...

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

20.

Is the sequence below arithmetic, geometric, neither, or both?

-5, 5, -5, 5, -5, 5, ...

a)

Arithmetic

b)

Geometric

c)

Neither

d)

Both

09-02 Arithmetic & Geometric Sequences

Total questions: 20

Worksheet time: 34mins

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