Write an equation to describe the sequence below use and to represent the position of a term in the sequence where n equals one for the first term 1, 4, 16

  an = 4^(n-1)

Step-by-step explanation:

The three given terms have a common ratio of 4:

  4/1 = 16/4 = 4

So, this can be described by the function for a geometric sequence:

  an = a1×r^(n -1)

where an is the n-th term, a1 is the first term (1) and r is the common ratio (4).

  an = 1×4^(n-1)

  an = 4^(n -1) . . . . . simplified

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.