Use the difference a+1 – an to show that the given sequence {an} is strictly increasing or strictly decreasing. n +00 1 5n – 4 n=1 an+1 - an = 4 strictly increasing (5n + 4)(5n – 1) 4 ; strictly increasing (5n – 4)(5n + 1) 4 (5n + 4)(5n ; strictly decreasing 1) 4 ; strictly decreasing (5n – 4)(5n + 1)' - 1 ; strictly decreasing (5n – 4)(5n + 4)'

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 1E
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Use the difference an+1 – an to show that the given sequence {an} is strictly increasing or strictly decreasing.
n
+00
5n – 4) n=1
аn+1 — ап %3
4
(5n + 4)(5n -
strictly increasing
1)
4
; strictly increasing
(5n
4)(5n + 1)
4
;; strictly decreasing
(5n + 4)(5n – 1)
-
4
; strictly decreasing
(5n – 4)(5n + 1)'
1
; strictly decreasing
(5n ·
- 4)(5n + 4)
Transcribed Image Text:Use the difference an+1 – an to show that the given sequence {an} is strictly increasing or strictly decreasing. n +00 5n – 4) n=1 аn+1 — ап %3 4 (5n + 4)(5n - strictly increasing 1) 4 ; strictly increasing (5n 4)(5n + 1) 4 ;; strictly decreasing (5n + 4)(5n – 1) - 4 ; strictly decreasing (5n – 4)(5n + 1)' 1 ; strictly decreasing (5n · - 4)(5n + 4)
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