Answer:
d = - [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
The sum to n terms of an arithmetic series is
[tex]S_n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 160, n = 25 and [tex]S_{25}[/tex] = 3500 , thus
[tex]\frac{25}{2}[/tex] [ (2 × 160) + 24d ] = 3500, that is
12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )
320 + 24d = 280 ( subtract 320 from both sides )
24d = - 40 ( divide both sides by 24 )
d = - [tex]\frac{40}{24}[/tex] = - [tex]\frac{5}{3}[/tex]
