Arithmetic Sequences and Their Terms

The video tutorial explains how to determine the 40th term in an arithmetic sequence. It begins by identifying whether a sequence is arithmetic by checking if the difference between terms is constant. The tutorial then introduces the explicit formula for sequences, a sub n = a sub 1 + (n - 1) * D, and demonstrates how to use it to find the 40th term. The instructor emphasizes the importance of following the order of operations to avoid mistakes in calculations. The tutorial concludes with a step-by-step example, ensuring students understand the process.

What is the main objective of the problem discussed in the video?

• To determine the 40th term in a sequence

• To find the first term in the sequence

• To find the sum of the first 40 terms

• To identify the common difference

How can you identify if a sequence is arithmetic?

• By checking if the terms are multiples of a number

• By checking if the terms are in descending order

• By checking if the difference between terms is constant

• By checking if the terms are in ascending order

What is the common difference in the sequence discussed?

• 2

• 5

• 4

• 3

Why is manually adding terms to find the 40th term not efficient?

• It is not accurate

• It takes too much time

• It requires a calculator

• It is too complicated

What is the explicit formula for finding the nth term in an arithmetic sequence?

• a_n = a_1 + n * D

• a_n = a_1 * n + D

• a_n = a_1 - (n - 1) / D

• a_n = a_1 + (n - 1) * D

What value should be plugged in for 'n' to find the 40th term?

• 1

• 40

• 2

• 39

What is the first term (a_1) in the sequence?

• 5

• 2

• 3

• 4

What is the result of 40 - 1 in the calculation?

• 38

• 39

• 40

• 41

What is the product of 39 and 2 in the calculation?

• 79

• 78

• 77

• 76

What is the 40th term in the sequence?

• 82

• 81

• 80

• 83