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Ashraf82

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What is the recursive formula for this geometric sequence 2, -10, 50, -250, .... ?

The recursive formula for this geometric sequence is:

[tex]a_{1}[/tex] = 2; [tex]a_{n}[/tex] = (-5) • [tex]a_{n-1}[/tex]

Step-by-step explanation:

To find the recursive formula for a geometric sequence:

  1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
  2. Find the common ratio. (The number you multiply or divide.)
  3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.

The recursive formula is:

[tex]a_{1}[/tex] = first term;  [tex]a_{n}[/tex] = r • [tex]a_{n-1}[/tex]  , where

  • [tex]a_{1}[/tex] is the first term in the sequence
  • [tex]a_{n-1}[/tex] is the term before the nth term  
  • r is the common ratio

∵ The geometric sequence is 2 , -10 , 50 , -250

∴ [tex]a_{1}[/tex] = 2

- To find r divide the 2nd term by the first term

∵ [tex]r=\frac{a_{2}}{a_{1}}[/tex]

∴ [tex]r=\frac{-10}{2}=-5[/tex]

- Substitute the values of [tex]a_{1}[/tex] and r in the formula above

∴  [tex]a_{1}[/tex] = 2; [tex]a_{n}[/tex] = (-5) • [tex]a_{n-1}[/tex]

The recursive formula for this geometric sequence is:

[tex]a_{1}[/tex] = 2; [tex]a_{n}[/tex] = (-5) • [tex]a_{n-1}[/tex]

Learn more:

You can learn more about the geometric sequence in brainly.com/question/1522572

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