Understanding Arithmetic Sequences and Patterns

The video tutorial explains how to identify and write equations for various types of sequences, including arithmetic sequences, sequences with alternating signs, perfect squares, and sequences involving fractions. It covers the concept of common difference, zero term, and how to derive general equations for sequences. The tutorial also provides examples and step-by-step methods to find specific terms in a sequence using the derived equations.

What is the common difference in the sequence 2, 4, 6, 8, 10?

• 2

• 1

• 3

• 4

Which equation represents the sequence 3, 6, 9, 12, 15?

• n

• 2n

• 4n

• 3n

What is the zero term for the sequence 1, 3, 5, 7, 9?

• 0

• -1

• 1

• 2

How do you represent a sequence with alternating signs?

• 2n-1

• (-1)^n

• n^2

• n+1

What is the equation for the sequence of perfect squares?

• 3n

• n+1

• 2n

• n^2

How do you find the general equation for a sequence involving fractions?

• Use only denominator

• Separate numerator and denominator

• Use only numerator

• Combine terms

What is the first term in the sequence 7, 10, 13, 16, 19?

• 16

• 13

• 10

• 7

How do you calculate the common difference in a sequence?

• Add first two terms

• Divide first term by second

• Subtract first term from second

• Multiply first two terms

What is the general formula for an arithmetic sequence?

• a_n = a_1 + (n-1)d

• a_n = n^2

• a_n = 2n-1

• a_n = (-1)^n

If the fourth term is 39 and the seventh term is 57, what is the common difference?

• 5

• 3

• 4

• 6