Answer:
a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16
equation of sequence: [tex]\boxed{\bold{a_n=7n-12}}[/tex]
Step-by-step explanation:
a₁ + a₂ + a₃ = 6
a₁ + a₁ + d + a₁ + 2d = 6
3a₁ + 3d = 6
a₁ + d= 2 ⇒ a₁ = 2 - d
a₄ = 16
a₁ + 3d = 16
2 - r + 3d = 16
2d = 14
d = 7
a₁ = 2-7 = -5
a₁ = -5, d = 7 ⇒ a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16
equation of arithmetic sequence:
[tex]a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}[/tex]
