Sequences and Series Worksheets

**Page 1**

1.

In the geometric series - 5, - 20, - 80 , . . . , S_{7} = ?

a. | $\frac{5}{3}$ | ||

b. | $\frac{16388}{3}$ | ||

c. | - 5461 | ||

d. | - 27305 |

[The common ratio.]

[Substitute

S

[Sum of

S

[Substitute

S

S

Correct answer : (4)

2.

What is the sum of the first 6 terms of the geometric series 1 + 4 + 16 + ... ?

a. | 1365 | ||

b. | 256 | ||

c. | 4098 | ||

d. | 4097 |

[The common ratio.]

[Substitute

S

[Sum of

S

[Substitute

S

So, the sum of the first 6 terms of the geometric series is 1365.

Correct answer : (1)

3.

The common difference in the arithmetic sequence 5, 6, 7, 8, . . . is ____.

a. | - 1 | ||

b. | $\frac{11}{2}$ | ||

c. | 1 | ||

d. | $\frac{1}{2}$ |

[First term.]

[Second term.]

[Find the common difference.]

So, the common difference is 1.

Correct answer : (3)

4.

The 19^{th} term of the arithmetic sequence 9.0, 9.5, 10.0, 10.5, . . . is ____.

a. | 18 | ||

b. | 48 | ||

c. | 46 | ||

d. | 29 |

[Find the common difference.]

= 9.5 - 9.0

[

= 0.5

[Formula for the

= 9.0 + 9 = 18

[Substitute

So, the 19

Correct answer : (1)

5.

The first term of an arithmetic sequence is 5 and the common difference is 3. The 4^{th} term is _____.

a. | 35 | ||

b. | 14 | ||

c. | 20 | ||

d. | 23 |

[Formula for the

[Substitute

= 5 + 9

= 14

So, the 4

Correct answer : (2)

6.

The first term of an arithmetic sequence is - 8 and the 11^{th} term is 22. What is the 12^{th} term ?

a. | 1 | ||

b. | 13 | ||

c. | 25 | ||

d. | 62 |

[Formula for the

[Substitute:

22 = - 8 + 10

30 = 10

3 =

[Substitute

= - 8 + 11(3)

= 25

So, the 12

Correct answer : (3)

7.

If 5 times the 5^{th} term is equal to the 6 times the 6^{th} term of an arithmetic sequence, then its 11^{th} term is_______

a. | 11 | ||

b. | 1 | ||

c. | - 1 |

[5(5

5(

[Substitute

5

0 =

0 =

So, the 11

Correct answer : (1)

8.

The common ratio of the geometric sequence 2, 10, 50, 250, . . . is ___.

a. | 5 | ||

b. | $\frac{1}{5}$ | ||

c. | 10 | ||

d. | $\frac{1}{10}$ |

[The common ratio formula.]

[Substitute

So, the common ratio of the sequence is 5.

Correct answer : (1)

9.

The common ratio of the geometric sequence 3, 0.3, 0.03, 0.003... is ___.

a. | 0.1 | ||

b. | 0.03 | ||

c. | 3 | ||

d. | 0.3 |

[Common ratio formula .]

[Substitute

So, the common ratio of the sequence is 0.1.

Correct answer : (1)

10.

The sum of the first 16 terms of the arithmetic series 2 + 6 + 10 + 14 + . . . is ______.

a. | 464 | ||

b. | 448 | ||

c. | 512 | ||

d. | 496 |

[Find

S

[Use the formula.]

S

[Substitute

S

S

So, the sum of the first 16 terms in the series is 512.

Correct answer : (3)