Question

Write an explicit formula for an, the nth term of the sequence 25,-5,1…

Answer 1

`a_n = 25((-1)/(5))^(n-1)`

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?

• 
  `a_n = a_1(b)^(n-1)`
• 
  `a_1` is the first term of the sequence
• 
  `b` is the common ratio (the number each term gets multiplied by)
• 
  `n` is the term number you want to find

To find the formula for this sequence, substitute the given values into the sequence equation.

`a_1` = 25

`b` = -1/5

∴ The formula is:
`a_n = 25((-1)/(5))^(n-1)`