The third term of an arithmetic sequence is −12 and the seventh term is 8. What is the sum of the first 10
terms?

5

Step-by-step explanation:

The n th term of an arithmetic sequence is

= 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

= [ 2a₁ + (n - 1)d ], thus

= [ (2 × - 22) + (9 × 5) ]

     = 5(- 44 + 45)

      = 5 × 1

       = 5