Question

PLEASE HELP ME!!!!!

Answer 1

When you subtract the y values you find that each increase in x decreases y by 4.

X is going from 4 to 82 which is 78 units.

78 x 4 = 312

Subtract 312 from the last y value:

209 - 312 = -103

The answer is -103

Answer 2

Answer:

When x = 82, y = -103

Step-by-step explanation:

So an arithmetic sequence is a sequence whose terms differ by a constant value. To find the value of the $n^{th}$ term we need to form an equation for the sequence.

Equation to the sequence

First we need to find the difference between the values of the sequence. In this case the difference is -4:

217 - 221 = -4,  209 - 213 = -4

So the equation is:

$n^{th}$ term = -4n + c

Now we need to find the c, so we substitute the $n^{th}$ term and the term number and solve the equation:

221 = (-4 x 1) + c

221 = -4 + c

c = 225

So the final equation is:

$n^{th}$ term = -4n +225

Finding the 82nd term

Now all we need to do is substitute into the equation and find the answer:

$n^{th}$ term = (-4 x 82) + 225

$n^{th}$ term = -328 +225

$n^{th}$ term = -103