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_9 - a_1
d = ---------
8
$$d = \frac{- a_{1} + a_{9}}{8}$$
a_9 - a_1
a_1 = a_9 - ---------*7
8
$$a_{1} = a_{9} - \frac{- a_{1} + a_{9}}{8} \cdot 7$$
$$d = \frac{-7 + 8}{8}$$
8 - 7
a_1 = 8 - -----*8
8
$$a_{1} = \left(-1\right) \frac{-7 + 8}{8} \cdot 8 + 8$$
$$d = \frac{1}{8}$$
$$a_{1} = 7$$
n*(a_1 + a_n)
S = -------------
2
$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$
9*(7 + 8)
S9 = ---------
2
$$S_{9} = \frac{9 \cdot \left(7 + 8\right)}{2}$$
$$S_{9} = \frac{135}{2}$$