Exploring Arithmetic Sequences and Their Explicit Formulas

The video tutorial covers arithmetic sequences, explaining their properties and how to identify them. It provides examples and non-examples to illustrate the concept of a common difference. The tutorial guides viewers through determining if a sequence is arithmetic and writing the explicit formula. It also demonstrates how to find specific terms in a sequence using the formula.

What is an explicit formula for an arithmetic sequence?

• a_n = a_1 * n / d

• a_n = a_1 + (n - 1) * d

• a_n = a_1 / (n - 1) + d

• a_n = a_1 - (n + 1) * d

What does 'n' represent in the formula of an arithmetic sequence?

• The total number of terms

• The nth term

• The first term

• The common difference

What is the common difference in the sequence 1, 3, 5, 7?

• 1

• 2

• 3

• 4

Which of the following sequences is not arithmetic?

• 2, 4, 6, 8

• 5, 10, 15, 20

• 1, 4, 9, 16

• 1, 2, 3, 4

What does the common difference in an arithmetic sequence indicate?

• The increment between any two consecutive terms

• The quotient of any two consecutive terms

• The product of any two consecutive terms

• The decrement between any two consecutive terms

How do you determine the first term in the explicit formula for an arithmetic sequence?

• It is the first term of the sequence.

• It is the sum of the first two terms.

• It is the difference between the first two terms.

• It is the product of the first two terms.

What is the explicit formula for an arithmetic sequence where the first term is 3 and the common difference is 2?

• a_n = 3 + (n - 1) * 2

• a_n = 3 / (n - 1) * 2

• a_n = 3 + 2n

• a_n = 3 * (n - 1) + 2

Which of the following is a correct step in deriving the explicit formula for an arithmetic sequence?

• Subtract the common difference from the first term.

• Divide the first term by the common difference.

• Multiply the common difference by (n - 1) and add to the first term.

• Add the first term to the product of the common difference and n.

What is the 52nd term of an arithmetic sequence with a first term of -5 and a common difference of -4?

• -213

• -209

• -201

• -217

Is the sequence 3, 7, 11, 19 arithmetic?

• Only partially

• Yes

• No

• Cannot be determined