Arithmetic Sequences and Their Properties

The video tutorial explains how to find the 27th term of an arithmetic sequence using a specific formula. It begins by introducing the sequence and the formula for finding the nth term. The common difference is calculated, and the formula is applied to find the 27th term. The process involves simplifying the expression to arrive at the result, which is -97. The tutorial concludes with a summary of the steps taken.

What is the formula used to find the nth term of an arithmetic sequence?

• a_n = a_1 / (n - 1) * d

• a_n = a_1 * n + d

• a_n = a_1 - (n - 1) * d

• a_n = a_1 + (n - 1) * d

What is the first term (a_1) of the given sequence?

• 3

• 7

• -1

• -5

How is the common difference (d) determined in an arithmetic sequence?

• By subtracting any term from the previous term

• By adding the first and last terms

• By dividing the last term by the first term

• By multiplying the first term by the number of terms

What is the common difference (d) in the sequence 7, 3, -1, -5?

• 3

• -4

• 4

• -3

What is the value of n when finding the 27th term of the sequence?

• 25

• 26

• 28

• 27

What operation is performed first when simplifying the expression for the 27th term?

• Division

• Addition

• Subtraction

• Multiplication

What is the result of 26 times the common difference in the sequence?

• 100

• -104

• -100

• 104

What is the final value of the 27th term in the sequence?

• 100

• -97

• -100

• 97

Which of the following is NOT a step in finding the 27th term of the sequence?

• Multiplying the common difference by 27

• Calculating the common difference

• Identifying the first term

• Adding the result to the first term

What is the purpose of using the arithmetic sequence formula in this context?

• To find the sum of the sequence

• To determine the nth term

• To calculate the average of the sequence

• To identify the last term