Skip to main content
Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblema 101
Capitolo 9, Problema 101

Write the first five terms of the sequence whose first term is 9 and whose general term is
Formula defining a sequence where each term depends on the previous term's parity with two different expressions.
for n≥2.

Guida verificata passo dopo passo
1
Identify the first term of the sequence: \( a_1 = 9 \). This is given directly in the problem.
Determine the rule for finding the next term \( a_n \) based on the previous term \( a_{n-1} \): if \( a_{n-1} \) is even, then \( a_n = \frac{a_{n-1}}{2} \); if \( a_{n-1} \) is odd, then \( a_n = 3a_{n-1} + 5 \).
Calculate the second term \( a_2 \) by checking if \( a_1 = 9 \) is even or odd. Since 9 is odd, use the odd term formula: \( a_2 = 3 \times 9 + 5 \).
Calculate the third term \( a_3 \) by checking if \( a_2 \) is even or odd, then apply the corresponding formula.
Repeat the process for the fourth and fifth terms, each time checking the parity (even or odd) of the previous term and applying the appropriate formula to find \( a_4 \) and \( a_5 \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Sequences and Terms

A sequence is an ordered list of numbers where each number is called a term. The first term is given, and subsequent terms are found using a rule or formula. Understanding how to identify and write terms is fundamental to working with sequences.
Video consigliato:
8:22
Introduction to Sequences

Recursive Definition of Sequences

A recursive sequence defines each term based on the previous term(s). Here, the nth term depends on the (n-1)th term with different rules depending on whether the previous term is even or odd. Recognizing and applying recursive rules is key to generating terms.
Video consigliato:
6:40
Arithmetic Sequences - Recursive Formula

Parity (Even and Odd Numbers)

Parity refers to whether an integer is even or odd. This property affects the rule used to find the next term in the sequence. Knowing how to determine parity helps decide which formula to apply for each term.
Video consigliato:
4:47
The Number e
Pratica correlata
Domanda del libro di testo

Use the formula an=4+(n−1)(−7)a_n=4+(n-1)(-7) to find the eighth term of the sequence 4,−3,−10,…4, −3, −10,…

821
views
Domanda del libro di testo

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood for three consecutive years?

634
views
Domanda del libro di testo

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood two years in a row?

806
views
Domanda del libro di testo

Solve: x/(x−3)=2x/(x−3)−5/3

734
views
Domanda del libro di testo

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of no flooding for four consecutive years?

773
views