Question

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

Answer 1

Answer:

  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 2

Answer:

$-4*(n-1$  with n=1,2.3,4....

Step-by-step explanation:

the sequence is 3, -12, 48, -192,...

This the negative in every second term indicates that the previous term is multiplied by negative number. We can also determine the common factor by taking -12, 48, 192 and dividing them by 4, therefore we will get the previous term. If we mutliply the 3 with -4 we get -12, if we multiply -12 with -4 we get 48, if we mutliply 48 by -4 we get -192 and so forth.

The recursive rule if n is the first term is:

$=-4*(n-1)$

with n=1,2,3,  ...