Step-by-step explanation:
a linear or arithmetic sequence has a start value as first term, and then every following term is created by adding the same constant to the previous term.
a1 = a
a2 = a1 + c = a + c
a3 = a2 + c = a + c + c = a + 2c
a4 = a3 + c = a + c + c + c = a + 3c
...
as we can easily see
an = an-1 + c = a + (n-1)c
in our case
a3 = 17 = a + 2c
a = 17 - 2c
a45 = 269 = a + 44c = 17 - 2c + 44c = 17 + 42c
252 = 42c
c = 6
a = 17 - 2c = 17 - 2×6 = 17 - 12 = 5
so,
an = 5 + (n-1)×6
