Question

The recursive equation for t(n)=4.5n-8

Answer 1

The student seems confused between a linear and a quadratic equation. The provided equation is linear (t(n) = 4.5n - 8), while the supporting information describes how to solve a quadratic equation using the quadratic formula with specified coefficients.

Step-by-step explanation:

The question posed by the student pertains to a recursive equation, which is a formula that defines each term of a sequence using preceding terms. However, the recursive equation mentioned (t(n) = 4.5n - 8) seems to be a simple linear equation rather than a recursive one. The student may be asking for a recursive form, but has provided a linear formula instead.

The additional information provided references a quadratic equation where the coefficients a, b, and c are given as 4.90, ±14.3, and ±20.0, respectively. The general form of a quadratic equation is at² + bt + c = 0. The solutions to this quadratic equation can be found using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). To find the solutions to the given quadratic equation, the values of a, b, and c would be substituted into the quadratic formula and the resulting expression solved.

For clarity, it seems there might be some confusion in the question as it mixes linear and quadratic equations. It is important to correctly identify the type of equation and its coefficients to proceed with finding a solution.

Answer 2

t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5

Step-by-step explanation:

t(n)=4.5n-8

Let find the sequence

Plug in n=1,2,3,4.....

n=1 t(1)=4.5(1) -8= -3.5

n=2 t(2)=4.5(2) -8= 1

n=3 t(3)=4.5(3) -8= 5.5

n=4 t(4)=4.5(4) -8= 10

so sequence is -3.5, 1, 5.5, 10................

Now we find the common difference

1 - (-3.5) = 4.5

5.5-1 = 4.5

10 - 5.5 = 4.5

common difference d = 4.5

Formula for recursive function is

t(n) = t(n-1) + d

We got d= 4.5

t(n) = t(n-1) + 4.5 , also t(1) = -3.5