Question

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

Answer 1

`-4*(n-1` with n=1,2.3,4....

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, ...

Answer 2

a[1] = 3; a[n] = -4a[n-1]

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].

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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.