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e3r6a2n1dz60

Answered question

2022-03-09

Write a formula or rule that generates the terms of each of the following sequences that begin with the given list. Begin indexing at

n = 1

.
a)

a_{n} = - 5, 12, - 19, 26, - 33, \dots

b_{n} = 3, 9, 27, 81, 243, \dots

c_{n} = \frac{- 5}{3}, \frac{12}{9}, \frac{- 19}{27}, \frac{26}{81}, \frac{- 33}{243}, \dots

Answer & Explanation

enimane69r

Beginner2022-03-10Added 1 answers

(a) $a_{n} = - 5, 12, - 19, 26, - 33, \dots$
Let $a_{1} = - 5$
$a_{n} = {\begin{cases} | a_{n - 1} + 7, i f n i s e v e n | \\ - (| a_{n - 1} | + 7), i f n i s o d d \end{cases}$
(b) $b_{n} = 3, 9, 27, 81, 243, \dots$
$b_{n} = 3^{n}$

Painiaerocaaph

Beginner2022-03-11Added 2 answers

3) $c_{n} = \frac{- 5}{3}, \frac{12}{9}, \frac{- 19}{27}, \frac{26}{81}, \frac{- 33}{243}, \dots$
Let $a_{1} = - 5$
then, $a_{n} = \frac{a_{n}}{b_{n}}$
$c_{n} = {\begin{cases} \frac{| a_{n - 1} | + 7}{3^{n}}, i f n i s e v e n \\ - \frac{| a_{n - 1} | + 7}{3^{n}}, i f n i s o d d \end{cases}$

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