   Chapter 11.1, Problem 73E

Chapter
Section
Textbook Problem

# Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?73. a n = 1 2 n + 3

To determine

Whether sequence is increasing, decreasing, not monotonic and bounded or not.

Explanation

Given:

The sequence is an=12n+3 . (1)

Definition used:

(1) The sequence {an} is increasing if an<an+1 for all n1 . That is, a1<a2<a3<... .

(2) The sequence {an} is decreasing and an>an+1 for all n1 . That is, a1>a2>a3>... .

(3) If the sequence is either increasing or decreasing, then the sequence is called monotonic; otherwise it is not monotonic.

(4) If {an} is the sequence with manM for m,M , then the sequence is bounded.

Calculation:

Check whether the sequence is increasing, decreasing or not monotonic.

Obtain the (n+1)th term of the sequence by substituting n+1 for n in equation (1).

an+1=12(n+1)+3=12n+2+3=12n+5<12n+3

Therefore, an>an+1 for all n1

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