The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Geometric and recursive functions
The general explicit formula for a geometric sequence is expressed as:
Given the following recursive functions:
[tex]a_1=-6\\
a_n=a_{n-1}\cdot\frac{1}{4} [/tex]
Get the next two terms:
[tex]a_2=a_{1}\cdot\frac{1}{4} \\
a_2=-6\cdot\frac{1}{4} \\
a_2=\frac{-3}{2} [/tex]
For the third term:
[tex]a_3=a_{2}\cdot\frac{1}{4} \\
a_3=\frac{-3}{2} \cdot\frac{1}{4} \\
a_3=\frac{-3}{8} [/tex]
The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]
The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Learn more on explicit functions here: https://brainly.com/question/10308651
