Quiz about Arithmetic and Geometric Sequences and Series Review

Question 1

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

Accepted Answer

arithmetic (common difference d = 5)

Answer

geometric (common ratio r = 5)

Answer

neither

Question 2

Describe the sequence, find the 5th term, and write the rule

Accepted Answer

arithmetic, a₅= 0, a_n = 2n - 10

Answer

geometric, a₅ = 2, a_n = 2n - 10

Answer

geometric, a₅ = 0, a_n = -10n + 2

Answer

arithmetic, a₅ = 2, a_n = -10n + 2

Question 3

The next term of the sequence 2,4,8,16 is

Accepted Answer

32

Answer

64

Answer

108

Answer

20

Question 4

Find the 22nd term of the following sequence:
5, 8, 11, ...

Accepted Answer

68

Answer

14

Answer

63

Answer

71

Question 5

Calculate the sum of the first 15 terms of the arithmetic sequence where $$a_1 = 7$$ and $$d = 3$$ .

Accepted Answer

345

Answer

315

Answer

330

Answer

360

Question 6

Find the common difference: a₂ = 6 and a₆ = -14

Accepted Answer

-5

Answer

-1

Answer

-2

Answer

2

Question 7

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...?

Accepted Answer

18,475

Answer

1,600

Answer

18,235

Answer

19,125

Question 8

Given the geometric sequence $$0.2, -1, 5, -25, ...$$

Find $$a_{10}$$

Accepted Answer

-390,625

Answer

390,625

Answer

1,953,125

Answer

78,125

Question 9

Evaluate the geometric series $$-3+15-75+375..., =8$$

Accepted Answer

195,312

Answer

-65,104

Answer

292,969

Answer

-130,208

Question 10

The sum of an infinite Geometric series is given by:

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 11

Find the sum of the first 50 numbers in this sequence:

$$\frac{1}{2}+\ 1+\frac{3}{2}+2+\frac{5}{2}+\ 3+\.\ .\ .$$

Accepted Answer

637.5

Answer

635.5

Answer

625

Answer

625.5

Question 12

Evaluate the infinite geometric series:

1 + 1/5 + 1/25 + ...

Accepted Answer

5/4

Answer

9/5

Answer

5/6

Answer

65/27

Question 13

Evaluate the infinite geometric series:

3 - 2 + 4/3 - 8/9 + ...

Accepted Answer

9/5

Answer

5/4

Answer

5/6

Answer

65/27

Question 14

Find the sum of the infinite geometric series, if it exists. $$\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+...$$

Accepted Answer

Does Not Exist

Answer

205

Answer

19.5

Answer

108.75

Question 15

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

Accepted Answer

17

Answer

18

Answer

15

Answer

14

Question 16

Write the explicit formula for the geometric sequence.

Accepted Answer

a_n = 3(-4)^n-1

Answer

a_n = 4(3)^n-1

Answer

a_n = 3(4)^n-1

Answer

a_n = -4(3)^n-1

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