GeoOrArith2.hs

main = interact $ show . f . map (map read . words) . lines

f :: [[Int]] -> Int
f ([n]:xs:_)
  | isArith xs = nthArith n xs
  | otherwise  = nthGeom  n  xs

isArith :: [Int] -> Bool
isArith (a:b:c:_) = b - a == c - b

nthArith :: Int -> [Int] -> Int
nthArith n (a:b:_) = seq !! n
  where
    seq = [a, a+(b-a)..]

nthGeom :: Int -> [Int] -> Int
nthGeom n (a:b:_) = seq !! n
  where
    seq = geoFrom a b (b `div` a)

geoFrom :: Int -> Int -> Int -> [Int]
geoFrom n n' m = seq
  where
    seq
      | signum n /= signum n' = n:map (*m) seq
      | n < n'                = n:map (*m) seq
      | otherwise             = decreasing n n'

decreasing n n' = seq
  where
    seq = n:map (`div` d) seq

    d = n `div` n'