Identify the type of sequence shown in the table below and select the appropriate response.

n: 1, 2, 3, 4, 5
f(n): 12, -36, 108, -324, 972

a) arithmetic sequence; common difference is -48

b) arithmetic sequence; common difference is 144

c) geometric sequence; common ratio is -3

d) geometric sequence; common ratio is 3

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions