Respuesta :

Answer:

a₉ = 50

Step-by-step explanation:

The sum to n terms of an arithmetic series is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term, d is the common difference and n the number of terms

Here a₁ = - 6, S₃₀ = 2865, n = 30 and d has to be found

[tex]\frac{30}{2}[/tex] [ (2 × - 6) + 29d ] = 2865 ( divide both sides by 15 )

- 12 + 29d = 191 ( add 12 to both sides )

29d = 203 ( divide both sides by 29 )

d = 7

The nth term is

[tex]a_{n}[/tex] = a₁ + (n - 1)d , then

a₉ = - 6 + (8 × 7) = - 6 + 56 = 50