Exploring the Basics of Sequences and Series

What symbol is typically used to denote sequences in mathematical notation?

• Angle brackets

• Parentheses

• Curly braces

• Square brackets

What does the subscript 'n' in 'a sub n' signify in the context of sequences?

• It represents a specific term number.

• It is just a placeholder with no specific meaning.

• It indicates the total number of terms.

• It denotes the sequence is infinite.

What does the term 'a sub 1' typically represent in a sequence?

• The average value of the sequence

• The sum of all terms

• The last term

• The first term

How does the order of terms affect the identity of a sequence?

• Order does not matter in sequences.

• Order is only relevant when using explicit formulas.

• Changing the order creates a different sequence.

• Order only matters in finite sequences.

What does an ellipsis at the end of a sequence indicate?

• The sequence has no specific pattern.

• The pattern of terms continues indefinitely.

• The sequence stops abruptly.

• The sequence is finite.

What is the difference between infinite and finite sequences?

• Infinite sequences have a definite end, finite do not.

• There is no difference; the terms are used interchangeably.

• Finite sequences continue forever, infinite do not.

• Infinite sequences continue indefinitely, finite have an end.

What is the purpose of an explicit formula in the context of sequences?

• To visualize the sequence graphically.

• To calculate the sum of all terms in the sequence.

• To find any term in the sequence without listing all prior terms.

• To determine the next term based on the previous term.

How can you find the 12th term of a sequence with an explicit formula?

• By graphing the first 11 terms and extrapolating.

• By multiplying the first term by 12.

• By setting n=12 in the formula.

• By adding the first 11 terms.

If a sequence is described by the formula 'a sub n = 2^n', what is the fifth term?

• 10

• 32

• 16

• 25

What does a negative exponent in a sequence formula indicate about the sequence's terms?

• The terms are zero.

• The terms are fractions.

• The terms are negative.

• The terms are decreasing.