Решение: a 10 − ? a_{10} - ? a 10 − ? { a 1 + a 2 + . . . + a 9 9 = 19 ⇒ a 1 + . . . + a 9 = 9 ⋅ 19 ; a 1 + . . . + a 10 10 = 20 ⇒ a 1 + . . . + a 10 = 10 ⋅ 20. \left\{\begin{matrix} \frac{a_{1} + a_{2} + . . . + a_{9}}{9} = 19 \Rightarrow a_{1} + . . . + a_{9} = 9 \cdot 19 ; \\ \frac{a_{1} + . . . + a_{10}}{10} = 20 \Rightarrow a_{1} + . . . + a_{10} = 10 \cdot 20 . \end{matrix}\right. { 9 a 1 + a 2 + ... + a 9 = 19 ⇒ a 1 + ... + a 9 = 9 ⋅ 19 ; 10 a 1 + ... + a 10 = 20 ⇒ a 1 + ... + a 10 = 10 ⋅ 20. { a 1 + . . . + a 9 = 171 a 1 + . . . + a 10 = 200 ∣ ⇒ a 10 = 200 − 171 = 29. \left\{\begin{matrix} a_{1} + . . . + a_{9} = 171 \\ a_{1} + . . . + a_{10} = 200 \end{matrix}\right | \Rightarrow a_{10} = 200 - 171 = 29 . { a 1 + ... + a 9 = 171 a 1 + ... + a 10 = 200 ⇒ a 10 = 200 − 171 = 29.
Ответ: 29
Источник : ФИПИ