Domanda del libro di testo
Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence. 3, 12, 48, 192, ...
1226
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 9, Problema 17
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a1=4 and an=2an-1 + 3 for n≥2
Guida verificata passo dopo passo1
Identify the first term of the sequence, which is given as \(a_1 = 4\).
Use the recursive formula \(a_n = 2a_{n-1} + 3\) to find the second term by substituting \(n=2\): calculate \(a_2 = 2a_1 + 3\).
Find the third term by substituting \(n=3\) into the recursive formula: calculate \(a_3 = 2a_2 + 3\).
Find the fourth term by substituting \(n=4\) into the recursive formula: calculate \(a_4 = 2a_3 + 3\).
List the first four terms as \(a_1\), \(a_2\), \(a_3\), and \(a_4\) after calculating each term step-by-step using the recursive formula.
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:
4mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Recursive Sequence Definition
A recursive sequence is defined by specifying the first term(s) and a formula that relates each term to one or more previous terms. Understanding how to use the given formula to find subsequent terms is essential for generating the sequence.
Video consigliato:
6:40
Arithmetic Sequences - Recursive Formula
Substitution Method for Finding Terms
To find terms in a recursive sequence, substitute the previous term(s) into the recursive formula step-by-step. This process involves calculating each term in order, starting from the initial term, to determine the next terms.
Video consigliato:
04:03Choosing a Method to Solve Quadratics
Arithmetic Operations and Order of Evaluation
Accurate calculation of each term requires careful application of arithmetic operations like multiplication and addition, following the correct order of operations. This ensures the sequence values are computed correctly at each step.
Video consigliato:
6:40Arithmetic Sequences - Recursive Formula
Pratica correlata
Domanda del libro di testo
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.
623
views
Domanda del libro di testo
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a1 = 7, d = 5.
932
views
Domanda del libro di testo
Find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2
1257
views
Domanda del libro di testo
Use mathematical induction to prove that each statement is true for every positive integer n. 1 + 2 + 22 + ... + 2n-1 = 2n - 1
705
views
Domanda del libro di testo
Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x²+2y)4
738
views