Enter a recursive rule for the geometric sequence. 3, −12, 48, −192, 

  a[1] = 3; a[n] = -4a[n-1]

Step-by-step explanation:

The first term is 3, so that is the first part of the recursive rule: a[1] = 3.

Each term is -4 times the previous term, so that is the second part of the recursive rule: a[n] = -4a[n-1].

You know a geometric sequence has a common ratio. That ratio can be found by dividing any term by the one before: -12/3 = -4. This is the value that each term is multiplied by to get the next term.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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