Answer: -273
Step-by-step explanation: To determine the 72nd term, we will want use our explicit formula which is shown below.
[tex]^{a}n = ^{a}1 + (n - 1)d[/tex]
Since we want to find the 72nd term, the [tex]^{a}n[/tex]
in the formula will be changed to [tex]^{a} 72[/tex].
Also, the 72 will be substituted in for the n
that is inside the set of parentheses.
Then [tex]^{a} 1[/tex] will be the 1st term given in our sequence or 11.
Lastly, the d outside the parentheses is the difference between
each of the terms in the sequence which is -4.
So we now have [tex]^{a} 72 = 11 + (72 - 1)(-4)[/tex].
Now we have all the information we need.
Now we can simplify from here.
Make sure to apply your order of operations because
this is where a lot of students make mistake.
Start simplifying inside the parentheses!
(72 - 1) is going to be 70.
So we have [tex]^{a} 72 = 11 + (71)(-4)[/tex].
Then, we have to multiply before we add.
So (71)(-4) is going to be -284.
So we have [tex]^{a} 72 = 11 + (-284)[/tex].
Solving from here, 11 + (-284) simplifies to -273.
This means that the 72nd term of this sequence is -273.
