Answer:
5
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = - 12 and a₇ = 8 , then
a₁ + 2d = - 12 → (1)
a₁ + 6d = 8 → (2)
Subtract (1) from (2) term by term
4d = 20 ( divide both sides by 4 )
d = 5
Substitute d = 5 into (1)
a₁ + 10 = - 12 ( subtract 10 from both sides )
a₁ = - 22
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], thus
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] [ (2 × - 22) + (9 × 5) ]
= 5(- 44 + 45)
= 5 × 1
= 5
