Question

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

Answer 1

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.

Explanation:

A) A sequence is an ordered list of numbers, letters, colors, or other objects. It is essentially a pattern.

B)
`n \to \infty (a_n) = 8` shows n approaching infinity. This means n, the term numbers of
`a_n`, get large. The fact that it equals 8 means that the terms of the sequence approach 8 as n gets large.

C)
`n \to \infty (a_n) = \infty` shows n approaching infinity. This means n, the term numbers of
`a_n`, get large. The fact that it equals infinity means that the terms of the sequence become large as n becomes large.