Answer:
d = [tex]\frac{1}{2}[/tex]
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 , thus
a₇ = a₁ + 6d
a₄ = a₁ + 3d
Given a₇ - 2a₄ = 1 , then
a₁ + 6d - 2(a₁ + 3d) = 1, that is
a₁ + 6d - 2a₁ - 6d = 1
- a₁ = 1 ( multiply both sides by - 1 )
a₁ = - 1
Given a₃ = 0 , then
a₁ + 2d = 0 , thus
- 1 + 2d = 0 ( add 1 to both sides )
2d = 1 ( divide both sides by 2 )
d = [tex]\frac{1}{2}[/tex]
