Answer:
4075
Step-by-step explanation:
The n th term of an arithmetic series is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference, hence
a + 3d = 17 → (1) and
a + 9d = 35 → (2)
Subtract (1) from (2) term by term
6d = 18 ( divide both sides by 6 )
d = 3 ← common difference
Substitute d = 3 into (1)
a + 9 = 17 ( subtract 9 from both sides )
a = 8 ← first term
The sum to n terms of an arithmetic series is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence
[tex]S_{50}[/tex] = 25 [ 16 + (49 × 3 ) ]
= 25 × 163
= 4075
