Maths sequence and series help! 10pts

The sum of the first 3 numbers of an arithmetic series is 12. if the 20th term is -32 find the first term and the common difference,

can you please also show the method and steps taken, thanks.

let first term = a
a + (a + d) +( a + 2d) = 12
3a + 3d = 12 divide by 3
a + d = 4..........(1)
a + 19d = - 32........(2) take (1) fro (2)
18d = - 36
d = - 36/18
d = - 2
Sub for d in (1)
a + - 2 = 4
a = 4 + 2
a = 6

First term 6
Common difference - 2

Arithmetic series:
x₁
x₂ = x₁ + k
x₃ = x₂ + k = x₁ + 2k
x₄ = x₃ + k = x₁ + 3k
...
xռ = xռ₋₁ + k = x₁ + (n-1)k

"The sum of the first 3 numbers of an arithmetic series is 12."
x₁ + x₂ + x₃ = 12
x₁ + (x₁+k) + (x₁+2k) = 12
3x₁ + 3k = 12
x₁ + k = 4

"the 20th term is -32"
x₂₀ = x₁ + 19k = -32

subtract equations to eliminate the x₁ term:
x₁ + 19k = -32
x₁ + k = 4
-----------------------
18k = -36

k = -2

by substitution,
x₁ + (-2) = 4
x₁ = 6

a + a + d + a + 2d = 12
a + 19d = -32

3a + 3d = 12
a + d = 4

18d = -36
d = -2

a = 6

The first term is 6, and the common difference is -2.