Arithmetic and Geometric Sequences

The video tutorial covers arithmetic and geometric sequences, explaining their definitions, differences, and how to find terms using explicit formulas. It provides examples for both types of sequences, demonstrating step-by-step calculations to find specific terms. The tutorial emphasizes understanding the common difference in arithmetic sequences and the common ratio in geometric sequences, with practical examples to reinforce learning.

What is the common difference in an arithmetic sequence?

• The first term of the sequence

• The sum of all terms

• The ratio between consecutive terms

• The difference between consecutive terms

How do you find the nth term in an arithmetic sequence?

• Using the formula a * r^(n-1)

• By subtracting the common difference from the first term

• Using the formula a + (n-1)d

• By adding all previous terms

In the sequence 12, 23, 34, 45, what is the common difference?

• 10

• 12

• 13

• 11

What is the 25th term of the sequence 12, 23, 34, 45?

• 306

• 296

• 286

• 276

In the sequence 11, 7, 3, -1, what is the common difference?

• -3

• -4

• -5

• -6

What is the 10th term of the sequence 11, 7, 3, -1?

• -21

• -23

• -25

• -27

What is the common ratio in a geometric sequence?

• The ratio between consecutive terms

• The sum of all terms

• The difference between consecutive terms

• The first term of the sequence

How do you find the nth term in a geometric sequence?

• Using the formula a + (n-1)d

• Using the formula a * r^(n-1)

• By adding all previous terms

• By subtracting the common ratio from the first term

In the sequence 2, 6, 18, 54, what is the common ratio?

• 5

• 2

• 3

• 4

What is the 10th term of the sequence 2, 6, 18, 54?

• 78732

• 19683

• 59049

• 39366