Question

Write a rule for the geometric sequence with the given description

Answer 1

Answer:

a. $a_n = -3(5^{n - 1})$

b. $a_n = 72(3^{1 - n})$

Step-by-step explanation:

a.

$a_1 = -3$

$a_2 = -3(5^1)$

$a_3 = -3(5^2)$

Notice that in each term, the exponent of the 5 is 1 less than the term number.

The general term is

$a_n = -3(5^{n - 1})$

b.

$a_1 = 72$

$a_2 = 72(\dfrac{1}{3})^1$

$a_3 = 72(\dfrac{1}{3})^2$

Notice that in each term, the exponent of the 1/3 is 1 less than the term number.

The general term is

$a_n = 72(\dfrac{1}{3})^{n - 1}$

$a_n = 72(\dfrac{1}{3^{n - 1}})$

$a_n = 72(3^{1 - n})$