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 [tex]n^{th}[/tex] 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:
[tex]n^{th}[/tex] term = -4n + c
Now we need to find the c, so we substitute the [tex]n^{th}[/tex] term and the term number and solve the equation:
221 = (-4 x 1) + c
221 = -4 + c
c = 225
So the final equation is:
[tex]n^{th}[/tex] term = -4n +225
Finding the 82nd term
Now all we need to do is substitute into the equation and find the answer:
[tex]n^{th}[/tex] term = (-4 x 82) + 225
[tex]n^{th}[/tex] term = -328 +225
[tex]n^{th}[/tex] term = -103
