Question

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Answer 1

a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:
`\boxed{\bold{a_n=7n-12}}`

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:

`a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}`