Answer:
551
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex]( first + last)
The number of terms is
[tex]a_{n}[/tex] = a + (n - 1)d ← d is the common difference, a is the first term
d = 5 - 2 = 8 - 5 = 3, hence
2 + 3(n - 1) = 56
2 + 3n - 3 = 56
3n - 1 = 56 ⇒ 3n = 57 ⇒ n = 19
[tex]S_{19}[/tex] = [tex]\frac{19}{2}[/tex] ( 2 + 56 ) = 19 × 29 = 551
