Question

What is a sequence? A sequence is the product of an ordered list of numbers. A sequence is an unordered list of numbers. A sequence is the sum of an unordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach 8 as n becomes small. The terms an approach -infinity as 8 approaches n. The terms an approach infinity as 8 approaches n. The terms an approach infinity as n become large. The terms an approach 8 as n becomes large. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes small. The terms an become small as n becomes large. The terms an approach zero as n becomes large. The terms an become large as n becomes large. The terms an become small as n becomes small.

Answer 1

Answer:

• (a) A sequence is an ordered list of numbers.

• (b) The terms an approach 8 as n becomes large.

• (c) The terms an become large as n becomes large.

Step-by-step explanation:

A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. Sequences often have specific ways they relate and can be analyzed using products and sums to identify and work with sequences. For this multiple choice, choose the best answer that defines what a sequence is.

(a) What is a sequence?

• A sequence is the product of an ordered list of numbers. A
• sequence is an unordered list of numbers.
• A sequence is the sum of an unordered list of numbers.
• A sequence is an ordered list of numbers.
• A sequence is the sum of an ordered list of numbers.

When working with sequences, the notation  lim n → ∞ an = 8 is commonly used. n = 8 may change, but the rest of the notation usually stays the same. The limit is an operation which can be used on a sequence to describe the behavior of the sequence and all it terms even though it continues indefinitely.  We use n → ∞ to say as the sequence goes on forever or as it approaches infinity which is the largest value. The use of an = 8 means to the sequence begins to approach one value 8 as it continues forever.  For this multiple choice, choose the best answer that defines the notation.

(b) What does it mean to say that lim n → ∞ an = 8?

• The terms an approach 8 as n becomes small.
• The terms an approach -infinity as 8 approaches n.
• The terms an approach infinity as 8 approaches n.
• The terms an approach infinity as n become large.
• The terms an approach 8 as n becomes large.

Use the same information from above to answer C. Keep in mind n =  ∞ means an becomes very large.

(c) What does it mean to say that lim n → ∞ an = ∞?

• The terms an become large as n becomes small.
• The terms an become small as n becomes large.
• The terms an approach zero as n becomes large.
• The terms an become large as n becomes large.
• The terms an become small as n becomes small.