a_n - a_k
d = ---------
n - k
$$d = \frac{- a_{k} + a_{n}}{- k + n}$$
$$a_{1} = d \left(n - 1\right) + a_{n}$$
(-1 + n)*(a_n - a_k)
a_1 = a_n - --------------------
n - k
$$a_{1} = a_{n} - \frac{\left(- a_{k} + a_{n}\right) \left(n - 1\right)}{- k + n}$$
a_3 - a_1
d = ---------
2
$$d = \frac{- a_{1} + a_{3}}{2}$$
a_3 - a_1
a_1 = a_3 - ---------*1
2
$$a_{1} = a_{3} - \frac{- a_{1} + a_{3}}{2} \cdot 1$$
$$d = \frac{-15 + 5}{2}$$
5 - 15
a_1 = 5 - ------*2
2
$$a_{1} = 5 - \frac{-15 + 5}{2} \cdot 2$$
$$d = -5$$
$$a_{1} = 15$$
n*(a_1 + a_n)
S = -------------
2
$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$
3*(15 + 5)
S3 = ----------
2
$$S_{3} = \frac{3 \cdot \left(5 + 15\right)}{2}$$
$$S_{3} = 30$$