Answer:
see explanation
Step-by-step explanation:
The nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₅ is double a₇ , then
a₁ + 4d = 2(a₁ + 6d) , that is
a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )
4d = a₁ + 12d ( subtract 12d from both sides )
- 8d = a₁
The sum of n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , substitute values
[tex]S_{17}[/tex] = [tex]\frac{17}{2}[/tex] ( 2(- 8d) + 16d)
= 8.5(- 16d + 16d)
= 8.5 × 0
= 0
