观察下列图形中小正方形的个数，则第10个图中小正方形的个数为___.

由图知：各图对应正方形个数为\({a_1} = 3,{a_2} = 6,{a_3} = 10,{a_4} = 15,{a_5} = 21,...\)

所以\({a_2} - {a_1} = 3,{a_3} - {a_2} = 4,{a_4} - {a_3} = 5,{a_5} - {a_4} = 6,...,{a_n} - {a_{n - 1}} = n + 1\)，

故\({a_n} - {a_1} = 3 + 4 + 5 + 6 + ... + n + 1 = \frac{{\left( {n - 1} \right)\left( {n + 4} \right)}}{2}\left( {n \geqslant 2} \right)\)，则\({a_n} = \frac{{(n - 1)(n + 4)}}{2} + 3\)，

所以\({a_{10}} = \frac{{9 \times 14}}{2} + 3 = 66\).

故答案为：66

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