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 5

Capitolo 9, Problema 5

Write the first four terms of each sequence whose general term is given. a_n=(−3)ⁿ

Guida verificata passo dopo passo

Identify the general term of the sequence, which is given by $a_n = (-3)^n$.

Recall that the sequence terms are found by substituting $n = 1, 2, 3, 4, \ldots$ into the general term.

Calculate the first term by substituting $n=1$: $a_1 = (-3)^1$.

Calculate the second term by substituting $n=2$: $a_2 = (-3)^2$.

Calculate the third and fourth terms by substituting $n=3$ and $n=4$: $a_3 = (-3)^3$ and $a_4 = (-3)^4$.

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Sequences and General Terms

A sequence is an ordered list of numbers defined by a general term formula, an, which gives the nth term. Understanding how to use the general term allows you to find specific terms by substituting values of n.

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Geometric Sequences - General Formula

Exponents and Powers

Exponents indicate repeated multiplication of a base number. For example, (−3)^n means multiplying −3 by itself n times, which affects the sign and magnitude of each term in the sequence.

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Powers of i

Evaluating Terms of a Sequence

To find the first four terms, substitute n = 1, 2, 3, and 4 into the general term. This process involves careful calculation of powers and signs to correctly list the sequence's initial terms.

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Introduction to Sequences

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