Как найти сумму шестнадцати первых

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    a_n - a_k
d = ---------
      n - k  

$$d = frac{- a_{k} + a_{n}}{- k + n}$$

$$a_{1} = d left(n – 1right) + a_{n}$$

            (-1 + n)*(a_n - a_k)
a_1 = a_n - --------------------
                   n - k        

$$a_{1} = a_{n} – frac{left(- a_{k} + a_{n}right) left(n – 1right)}{- k + n}$$

    a_17 - a_1
d = ----------
        16    

$$d = frac{- a_{1} + a_{17}}{16}$$

             a_17 - a_1   
a_1 = a_17 - ----------*15
                 16       

$$a_{1} = a_{17} – frac{- a_{1} + a_{17}}{16} cdot 15$$

$$d = frac{-3 + 17}{16}$$

           17 - 3   
a_1 = 17 - ------*16
             16     

$$a_{1} = left(-1right) frac{-3 + 17}{16} cdot 16 + 17$$

$$d = frac{7}{8}$$

$$a_{1} = 3$$

3; 31/8; 19/4; 45/8; 13/2; 59/8; 33/4; 73/8; 10; 87/8; 47/4; 101/8; 27/2; 115/8; 61/4; 129/8; 17...

$$a_{1} = 3$$

$$a_{2} = frac{31}{8}$$

$$a_{3} = frac{19}{4}$$

$$a_{4} = frac{45}{8}$$

$$a_{5} = frac{13}{2}$$

$$a_{6} = frac{59}{8}$$

$$a_{7} = frac{33}{4}$$

$$a_{8} = frac{73}{8}$$

$$a_{9} = 10$$

$$a_{10} = frac{87}{8}$$

$$a_{11} = frac{47}{4}$$

$$a_{12} = frac{101}{8}$$

$$a_{13} = frac{27}{2}$$

$$a_{14} = frac{115}{8}$$

$$a_{15} = frac{61}{4}$$

$$a_{16} = frac{129}{8}$$

$$a_{17} = 17$$

    n*(a_1 + a_n)
S = -------------
          2      

$$S = frac{n left(a_{1} + a_{n}right)}{2}$$

      17*(3 + 17)
S17 = -----------
           2     

$$S_{17} = frac{17 cdot left(3 + 17right)}{2}$$

$$S_{17} = 170$$

$$a_{n} = d left(n – 1right) + a_{1}$$

$$a_{17} = 17$$