Find an explicit formula for the geometric sequence 96,24,6,1.5,...

96 / 4 ^n-1

Step-by-step explanation:

This is a geometric sequence with a first term of 96. The common ratio is the division of the 2nd term by the first term. This will be:

24/96 = 1/4

a = 96

r = 1/4

The formula will be:

ar ^n-1

= 96 × (1/4)^n-1

The concluding part is explained in the attached file.

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