(04.06 LC) Identify the type of sequence shown in the table below and select the appropriate response. (5 points)

n f(n)
1 48
2 −96
3 192
4 −384
5 768
a
Arithmetic sequence; common difference is 96

b
Arithmetic sequence; common difference is −144

c
Geometric sequence; common ratio is 3

d
Geometric sequence; common ratio is −2

d Geometric sequence; common ratio is −2

Step-by-step explanation:

Identifying Sequences

There are two possible types of sequences to choose from, Arithmetic and Geometric.

The arithmetic sequences are identified because each term is obtained by adding or subtracting a fixed number to the previous term. This number is called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

The given sequence is:

48, -96, 192, -384, 768,

To identify the type of sequence, we could try subtracting the second term from the first, the third from the second, etc. If those differences were constant, it would be an arithmetic sequence.

In this case, it's not necessary because the sign of the terms is alternating. It can only be possible with geometric sequences with a negative common ratio.

Dividing the second by the first term:

r = -96 / 48 = -2

Dividing the third by the second term:

r = 192 / -96 = -2

The rest of the divisions of successive terms lead to the same common ratio, thus, the answer is:

d  Geometric sequence; common ratio is −2

y=mx+b

step-by-step explanation:

m slope, b y-intercept

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24