Geometric and Arithmetic Sequences

The video tutorial provides a comprehensive guide on writing recursive formulas for arithmetic and geometric sequences. It explains the importance of identifying the starting value and the pattern based on previous terms. The tutorial includes examples of arithmetic sequences with common differences and geometric sequences with common ratios, demonstrating how to convert these into recursive formulas. The video concludes with a summary of the key points discussed.

What is the primary purpose of a recursive formula in sequences?

• To determine the starting point and pattern of a sequence

• To find the sum of all terms

• To calculate the average of terms

• To identify the last term in a sequence

In an arithmetic sequence, what is the common difference?

• The constant amount added to each term to get the next

• The sum of all terms

• The ratio of consecutive terms

• The difference between the first and last term

If a sequence starts at 3 and increases by 5, what is the recursive formula for the nth term?

• a_n = a_(n-1) - 5

• a_n = a_(n-1) + 3

• a_n = a_(n-1) + 5

• a_n = a_(n-1) * 5

In the sequence 15, 9, 3, -3, what is the common difference?

• -3

• 3

• -6

• 6

What is the first term of the sequence 15, 9, 3, -3?

• -3

• 15

• 3

• 9

What defines a geometric sequence?

• A sequence with increasing terms

• A sequence with decreasing terms

• A sequence with a common difference

• A sequence with a common ratio

In the sequence 1, 3, 9, 27, what is the common ratio?

• 3

• 27

• 9

• 1

What is the recursive formula for a geometric sequence starting at 1 with a common ratio of 3?

• a_n = a_(n-1) - 3

• a_n = a_(n-1) + 3

• a_n = 3 * a_(n-1)

• a_n = a_(n-1) / 3

In the sequence 192, 48, 12, 3, what is the common ratio?

• 3

• 1/3

• 4

• 1/4

What is the first term of the sequence 192, 48, 12, 3?

• 192

• 3

• 12

• 48