Answer:
-73
Explanation:
The first term is 5.
The common difference is -3.
The first term is given: 5
To find the next term, add the common difference.
The second term is 5 + (-3) = 2
The third term is 5 + (-3) + (-3) = -1
The fourth term is 5 + (-3) + (-3) + (-3) = -4
Notice that for each term, you start with 5 and you and -3 times 1 less than the number of the term.
The nth term is:
a_n = 5 + (-3)(n - 1)
a_n = 5 - 3n + 3
a_n = 8 - 3n
Let's test this expression for the first 4 terms:
a_1 = 8 - 3(1) = 5
a_2 = 8 - 3(2) = 2
a_3 = 8 - 3(3) = -1
a_4 = 8 - 3(4) = -4
Notice we get the same numbers we did above for the first 4 terms. This expression does work.
Now we find the 27th term:
a_27 = 8 - 3(27)
a_27 = -73