Answer:
The formula for the nth term of the sequence is [tex]A_n =250(\frac{2}{5})^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is always the same, called common ratio.
The equation is given by:
[tex]A_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and r is the common ratio.
250, 100, 40
First term is 250, so [tex]a_1 = 250[/tex]
Common ratio is [tex]r = \frac{40}{100} = \frac{100}{250} = \frac{2}{5}[/tex]
So
[tex]A_n = a_1q^{n-1}[/tex]
[tex]A_n =250(\frac{2}{5})^{n-1}[/tex]
The formula for the nth term of the sequence is [tex]A_n =250(\frac{2}{5})^{n-1}[/tex]
