Understanding Sequences and Series

This video introduces sequences, defining them as ordered lists of terms. It explains finite and infinite sequences, and how they can be considered functions with domains and ranges. The video demonstrates finding terms in sequences using formulas and recursive methods. It also covers arithmetic and geometric sequences, highlighting their patterns and differences.

What is a sequence in mathematics?

• A single number repeated

• A set of unrelated elements

• An ordered list of terms

• A random list of numbers

How can a finite sequence be identified?

• It is always increasing

• It has no terms

• It continues indefinitely

• It has a specific number of terms and then stops

What is the first term of the sequence defined by 3n - 5?

• 7

• 1

• -2

• 4

In a sequence where n is the exponent, what is the second term if the formula is 2^n + 1?

• 9

• 5

• 17

• 3

What does a recursive formula rely on to find a term in a sequence?

• Previous terms in the sequence

• The product of all terms

• The value of n

• The sum of all terms

If a sequence starts with 3 and follows the recursive formula a_n = 4a_(n-1) - 3, what is the second term?

• 3

• 9

• 12

• 33

What is a common difference in an arithmetic sequence?

• The difference between any two terms

• The difference between consecutive terms

• The sum of all terms

• The product of all terms

In an arithmetic sequence, if the first term is 37 and the second term is 31, what is the common difference?

• 6

• -6

• 31

• 37

What defines a geometric sequence?

• Subtracting a constant from each term

• Dividing by a constant to determine consecutive terms

• Adding a constant to each term

• Multiplying by a constant to determine consecutive terms

If a geometric sequence has a first term of 9 and a second term of 3, what is the common ratio?

• 3

• 9

• 1/9

• 1/3