Answer:
[tex]S _{19} = 760[/tex]
Step-by-step explanation:
[tex]a1 = 13 \\ a2 = 16 \\ d = a2 - a1 = 16 - 13 = 3 \\ d = 3 \\ a _{n} = l = 67 \\ [/tex]
now,
[tex]a _{n} = a + (n - 1) \times d \\ 67 = 13 + (n - 1) \times 3 \\ 67 = 13 + 3n - 3 \\ 67 - 13 + 3 = 3n \\ 57 = 3n \\ 3n = 57 \\ \\ n = \frac{57}{3} \\ \\ n = 19[/tex]
now the sum of the numbers
[tex]S _{n} = \frac{n}{2} (a + l) \\ \\ S _{19} = \frac{19}{2} (13 + 67) \\ \\ S _{19} = \frac{19}{2} (80) \\ \\ S _{19} = \frac{19}{2} \times 80 \\ \\ S _{19} = 19 \times 40 \\ S _{19} = 760[/tex]
