Question

What will be the first negative term in the sequence 87,84,81​

Answer 1

a₃₁

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

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 87 and d = - 3 , then

`a_(n)` = 87 - 3(n - 1) = 87 - 3n + 3 = 90 - 3n

To find when
`a_(n)` < 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