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

User Aamarks
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1 Answer

4 votes

Answer:


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)

User Szydan
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