Answer:
[tex]a_n = 25(\frac{-1}{5})^{n-1}[/tex]
Step-by-step explanation:
Each term in this sequence gets multiplied by -1/5, to get the subsequent term.
Thus, this sequence is a geometric sequence/progression.
⭐What is the formula for a geometric sequence?
- [tex]a_n = a_1(b)^{n-1}[/tex]
- [tex]a_1[/tex] is the first term of the sequence
- [tex]b[/tex] is the common ratio (the number each term gets multiplied by)
- [tex]n[/tex] is the term number you want to find
To find the formula for this sequence, substitute the given values into the sequence equation.
[tex]a_1[/tex] = 25
[tex]b[/tex] = -1/5
∴ The formula is: [tex]a_n = 25(\frac{-1}{5})^{n-1}[/tex]
