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 29
Capitolo 9, Problema 29

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. a1=-20, d = -4

Guida verificata passo dopo passo
1
Recall that the general term (nth term) of an arithmetic sequence can be written as \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference.
Identify the given values: the first term \(a_1 = -20\) and the common difference \(d = -4\).
Substitute these values into the general term formula to get \(a_n = -20 + (n - 1)(-4)\).
Simplify the expression inside the parentheses: \(a_n = -20 - 4(n - 1)\).
To find the 20th term, substitute \(n = 20\) into the formula: \(a_{20} = -20 - 4(20 - 1)\).

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:
3m

Concetti chiave

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

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This constant is called the common difference (d). Understanding this pattern is essential to write formulas and find specific terms.
Video consigliato:
5:17
Arithmetic Sequences - General Formula

General Term Formula of an Arithmetic Sequence

The general term (nth term) of an arithmetic sequence is given by the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. This formula allows direct calculation of any term without recursion.
Video consigliato:
5:17
Arithmetic Sequences - General Formula

Evaluating the nth Term

Once the general term formula is established, substituting the desired term number (like n=20) into the formula yields the specific term's value. This step involves simple arithmetic and is crucial for solving problems that ask for a particular term.
Video consigliato:
06:56
Nth Roots
Pratica correlata
Domanda del libro di testo

Find each indicated sum. ∑i=165i\(\sum\)_{i=1}^{6} 5i

845
views
Domanda del libro di testo

Use the Fundamental Counting Principle to solve Exercises 29–40. A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

643
views
Domanda del libro di testo

Use mathematical induction to prove that each statement is true for every positive integer n. n + 2 > n

682
views
Domanda del libro di testo

Use mathematical induction to prove that each statement is true for every positive integer n. ∑i=1n5⋅6i=6(6n−1)\(\sum\)_{i=1}^{n} 5 \(\cdot\) 6^i = 6(6^n - 1)

736
views
Domanda del libro di testo

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x+2)8

689
views
Domanda del libro di testo

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)6

687
views