Find the first several terms of a sequence with given two terms

The video tutorial explains how to find the first five terms of an arithmetic sequence given two terms, a_8 = 26 and a_12 = 42. It introduces the concept of arithmetic sequences and the common difference, d. The tutorial demonstrates how to calculate d by dividing the difference between the given terms by the number of intervals. Once d is found, the video shows how to backtrack to find the first term, a_1, and subsequently the first five terms of the sequence. The tutorial concludes with a brief mention of alternative methods to find a_1.

What is the main characteristic of an arithmetic sequence?

• The terms are all even numbers.

• The difference between consecutive terms is constant.

• The sum of the terms is always zero.

• The terms are all prime numbers.

If a_8 is 26 and a_12 is 42, what is the common difference in the sequence?

• 5

• 4

• 3

• 2

How do you calculate the common difference (d) using two known terms in an arithmetic sequence?

• Subtract the smaller term from the larger term and divide by the number of terms between them.

• Add the two terms and divide by 2.

• Multiply the two terms and divide by the number of terms between them.

• Subtract the larger term from the smaller term and divide by the number of terms between them.

What is the first term (a_1) of the sequence if a_8 is 26 and the common difference is 4?

• 4

• -2

• 0

• 2

Which of the following is the correct sequence of the first five terms given a_1 is -2 and the common difference is 4?

• -2, 2, 6, 10, 14

• 0, 4, 8, 12, 16

• 2, 6, 10, 14, 18

• -4, 0, 4, 8, 12