Approximate the solution to the equation above using three iterations of successive approximation. use the graph below as a starting point.

  x ≈ 1.683006

Step-by-step explanation:

There are many successive approximation techniques. For these functions, it seems to work to solve the equation for x:

  6^(-x) +4 = 3x -1

  6^(-x) +5 = 3x . . . . . . add 1

  (6^(-x) +5)/3 = x . . . .  divide by the coefficient of x

Then we can use the function ...

  f(x) = (6^(-x) +5)/3

to find a new value of x, given an initial value of x.

As we read the graph, the point where the curves cross is at about x=1.7, so that will be our initial starting point for iteration. The attachment shows the successive values of f(x) for three iterations. The third evaluation of f(x) gives an approximate root value of ...

  x ≈ 1.683006

i just took the test, the correct answer is .. 31.5 in.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for