Exploring Sequences and Series

What is the common difference in the arithmetic sequence 3, 7, 11, 15?

• 8

• 4

• 6

• 2

Identify whether the sequence 2, 6, 18, 54 is arithmetic or geometric.

• arithmetic

• quadratic

• geometric

• linear

Find the 10th term of the arithmetic sequence 5, 10, 15, ...

• 60

• 55

• 50

• 45

Calculate the sum of the first 20 terms of the series 1, 4, 7, ...

• 600

• 590

• 580

• 620

Determine if the series 1/2 + 1/4 + 1/8 + ... converges or diverges.

• oscillates

• remains constant

• diverges

• converges

What is the 5th term of the geometric sequence 3, 6, 12, ...?

• 60

• 36

• 24

• 48

Identify the first term and common ratio of the geometric sequence 5, 15, 45, ...

• First term: 5, Common ratio: 5

• First term: 10, Common ratio: 2

• First term: 15, Common ratio: 3

• First term: 5, Common ratio: 3

Find the sum of the first 15 terms of the arithmetic sequence 2, 5, 8, ...

• 300

• 400

• 345

• 250

Is the sequence 1, 1/2, 1/4, 1/8 convergent? If so, to what value?

• No, it diverges to infinity.

• Yes, it converges to 0.

• Yes, it converges to 1.

• Yes, it converges to -1.

What is the nth term formula for the arithmetic sequence 4, 9, 14, ...?

• a_n = 4n + 1

• a_n = 6n - 2

• a_n = 3n + 5

• a_n = 5n - 1