Question

Write an explicit formula for the sequence 4, -12, 36, -108

Answer 1

The sequence 4, -12, 36, -108 is a geometric sequence with a common ratio of -3. The explicit formula for the nth term an in this sequence is an = 4 × (-3)n-1.

Step-by-step explanation:

The sequence given is 4, -12, 36, -108, and it displays a pattern where each term is multiplied by -3 to get the next term. To write an explicit formula for this sequence, we need to find a relation that gives the nth term based on its position (n).

Let's denote the nth term as an. The first term a1 is 4, and each subsequent term is obtained by multiplying the previous term by -3. Therefore, we can describe the nth term using the following geometric sequence formula:

an = a1 × rn-1

where a1 is the first term and r is the common ratio. For this sequence, a1 = 4 and the common ratio r = -3. Thus:

an = 4 × (-3)n-1

Answer 2

n= any of the sequenced numbers x= value that is multiplied y = the new number in the sequence y = n (-x)

Step-by-step explanation:

Ex: y= 4 (-3)

y = -12

y = -12 (-3)

y = 36

y = 36(-3)

y = -108

y = - 108 (-3)

y = 324