Determine if the type of sequence of the following terms. 2, 5, 10, 17, 26, 37,
...
O Arithmetic
O Polynomial
O Neither
O Geometric
Question

B: polynomial

Step-by-step explanation:

The sequence given is;

2, 5, 10, 17, 26, 37,...

From this sequence, the first difference between consecutive terms is respectively;

3, 5, 7, 9, 11...

We can see that the differences gotten are not constant.

Now, let's find the second difference between the consecutive first differences respectively;

2, 2, 2, 2...

This second difference is constant and thus we can say that the terms form a quadratic sequence of the form;

f(x) = an² + bx + c

Where the quadratic coefficient is two times the second difference.

Thus;

2a = 2

a = 1

And where c is the 0th term.

Thus, this is a quadratic sequence. Since quadratic functions are 2nd degree polynomials, then this is said to be a polynomial sequence.

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!