What is the nth term of 4,7,12,19 asap i need

The correct answer is n²+3.

Explanation:

We find the first differences between terms:

7-4=3; 12-7=5; 19-12=7; 28-19=9.

Since these are different, this is not linear.

We now find the second differences:

5-3=2; 7-5=2; 9-7=2.

Since these are the same, this sequence is quadratic.

We use (1/2a)n², where a is the second difference:

(1/2*2)n²=1n².

We now use the term number of each term for n:

4 is the 1st term; 1*1²=1.

7 is the 2nd term; 1*2²=4.

12 is the 3rd term; 1*3²=9.

19 is the 4th term; 1*4²=16.

28 is the 5th term: 1*5²=25.

Now we find the difference between the actual terms of the sequence and the numbers we just found:

4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.

Since this is constant, the sequence is in the form (1/2a)n²+d;

in our case, 1n²+d, and since d=3, 1n²+3.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is