Sequences work please help
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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