Answer: -4, -14, -44, -134, -404
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Explanation:
The notation [tex]a_1 = -4[/tex] tells us that the first term is -4.
To generate the next term, we'll use the recursive rule [tex]a_n = 3*a_{n-1}-2[/tex] which is probably better written as [tex]a_n = 3*(a_{n-1})-2[/tex]. That rule says: "Whatever the previous term is, multiply by 3 and subtract off 2 to get the next term".
This means,
- 2nd term = 3*(1st term) - 2 = 3*(-4)-2 = -14
- 3rd term = 3*(2nd term) - 2 = 3*(-14)-2 = -44
- 4th term = 3*(3rd term) - 2 = 3*(-44)-2 = -134
- 5th term = 3*(4th term) - 2 = 3*(-134)-2 = -404
Therefore, the first five terms are: -4, -14, -44, -134, -404
