Ch. 8 - Sequences, Induction, and Probability

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

Problema 1

Capitolo 9, Problema 1

Write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Guida verificata passo dopo passo

Identify the general term of the sequence, which is given as $a_n = 7n - 4$, where $n$ represents the term number.

To find the first term ($a_1$), substitute $n = 1$ into the general term: $a_1 = 7(1) - 4$.

To find the second term ($a_2$), substitute $n = 2$ into the general term: $a_2 = 7(2) - 4$.

To find the third term ($a_3$), substitute $n = 3$ into the general term: $a_3 = 7(3) - 4$.

To find the fourth term ($a_4$), substitute $n = 4$ into the general term: $a_4 = 7(4) - 4$.

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Sequences and Terms

A sequence is an ordered list of numbers defined by a specific rule or formula. Each number in the sequence is called a term, and the position of a term is indicated by its index n. Understanding how to identify and write terms from a general formula is fundamental.

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Introduction to Sequences

General Term Formula

The general term formula, a_n, expresses the nth term of a sequence as a function of n. For example, a_n = 7n - 4 means to find the nth term, multiply n by 7 and subtract 4. This formula allows calculation of any term without listing all previous terms.

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Writing a General Formula

Evaluating Terms of a Sequence

To find specific terms, substitute values of n (starting from 1) into the general term formula. For the first four terms, calculate a_1, a_2, a_3, and a_4 by plugging in n = 1, 2, 3, and 4 respectively. This process helps generate the sequence explicitly.

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Introduction to Sequences

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