Answer:
a₃₁
Step-by-step explanation:
The terms have a common difference between consecutive terms, that is
d = 84 - 87 = 81 - 84 = - 3
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 87 and d = - 3 , then
[tex]a_{n}[/tex] = 87 - 3(n - 1) = 87 - 3n + 3 = 90 - 3n
To find when [tex]a_{n}[/tex] < 0 , solve
90 - 3n < 0 ( subtract 90 from both sides )
- 3n < - 90
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity, then
n > 30
Thus the 31st term will be the first negative term
