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 53
Capitolo 9, Problema 53

In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = 2n

Guida verificata passo dopo passo
1
Identify the general term of the sequence, which is given as an = 2n.
Recall the definitions: an arithmetic sequence has a constant difference between consecutive terms, and a geometric sequence has a constant ratio between consecutive terms.
Calculate the first few terms of the sequence by substituting values of n: for example, a_1 = 2^1 = 2, a_2 = 2^2 = 4, a_3 = 2^3 = 8.
Check if the difference between consecutive terms is constant: compute a_2 - a_1 and a_3 - a_2. If these are equal, the sequence is arithmetic.
If the differences are not constant, check the ratio of consecutive terms: compute \(\frac{a_2}{a_1}\) and \(\frac{a_3}{a_2}\). If these ratios are equal, the sequence is geometric and the common ratio is that value.

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:
2m

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 the difference between consecutive terms is constant. This constant is called the common difference. For example, in the sequence 3, 5, 7, 9, the common difference is 2.
Video consigliato:
5:17
Arithmetic Sequences - General Formula

Geometric Sequence

A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a fixed number called the common ratio. For example, in 2, 4, 8, 16, the common ratio is 2.
Video consigliato:
4:18
Geometric Sequences - Recursive Formula

General Term of a Sequence

The general term (an) of a sequence defines the nth term as a function of n. Understanding this formula helps identify the type of sequence and calculate specific terms, differences, or ratios. For example, an = 2^n defines each term as 2 raised to the power n.
Video consigliato:
4:45
Geometric Sequences - General Formula
Pratica correlata
Domanda del libro di testo

If you toss a fair coin six times, what is the probability of getting all heads?

617
views
Domanda del libro di testo

The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = n2 + 5

813
views
Domanda del libro di testo

Use the formula for nCr to solve Exercises 49–56. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

699
views
Domanda del libro di testo

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

995
views
Domanda del libro di testo

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

1618
views
Domanda del libro di testo

Find f(x + h) − f(x)/h and simplify. f(x) = x4+7

577
views