Domanda del libro di testo
Use the formula for nPr to evaluate each expression. 9P4
682
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 1
Write the first five terms of each geometric sequence. a1 = 5, r = 3
Guida verificata passo dopo passo1
Identify the first term \(a_1\) and the common ratio \(r\) of the geometric sequence. Here, \(a_1 = 5\) and \(r = 3\).
Recall the formula for the \(n\)-th term of a geometric sequence: \(a_n = a_1 \times r^{n-1}\).
Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = 5 \times 3^{2-1} = 5 \times 3\).
Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = 5 \times 3^{3-1} = 5 \times 3^2\).
Continue this process to find the fourth and fifth terms: \(a_4 = 5 \times 3^{4-1}\) and \(a_5 = 5 \times 3^{5-1}\).
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:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Geometric Sequence Definition
A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. This ratio remains the same throughout the sequence, creating a consistent pattern of growth or decay.
Video consigliato:
4:18
Geometric Sequences - Recursive Formula
Common Ratio (r)
The common ratio is the fixed factor by which each term in a geometric sequence is multiplied to get the next term. In this problem, the ratio is 3, meaning each term is three times the previous term, which determines how quickly the sequence grows.
Video consigliato:
5:57Graphs of Common Functions
Finding Terms of a Geometric Sequence
To find the nth term of a geometric sequence, use the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. Applying this formula allows you to calculate any term, including the first five terms as requested.
Video consigliato:
4:18Geometric Sequences - Recursive Formula
Pratica correlata
Domanda del libro di testo
Write the first four terms of each sequence whose general term is given. an = 7n - 4
1010
views
Domanda del libro di testo
Evaluate the given binomial coefficient.
627
views
Domanda del libro di testo
Write the first six terms of each arithmetic sequence. a1 = 200, d = 20
941
views
Domanda del libro di testo
Write the first four terms of each sequence whose general term is given. an=3n+2
831
views
Domanda del libro di testo
A statement Sn about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 3 + 4 + 5 + ... + (n + 2) = n(n + 5)/2
621
views