[tex]a_2 = 2 \\ a_6 = 22 \\ a_n = 222[/tex]
[tex]a_2 + 4r = a_6 \\ 2 + 4r = 22 \\ 4r = 20 | \div 4 \\ r = 5[/tex]
[tex]a_1 + r = a_2 \\ a_1 + 5 = 2 \\ \boxed{a_1 = - 3}[/tex]
[tex]a_n = a_1 + (n - 1) \times r \\ 222 = - 3 + (n - 1) \times 5 \\ 222 = - 3 + 5n - 5 \\ 222 = 5n - 8 \\ 5n = 230 | \div 5 \\ \boxed{ n = 46}[/tex]
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[tex]a_2 = 2 \\ a_6 = 22 \\ a_n = 222[/tex]
[tex]a_2 + 4r = a_6 \\ 2 + 4r = 22 \\ 4r = 20 | \div 4 \\ r = 5[/tex]
[tex]a_1 + r = a_2 \\ a_1 + 5 = 2 \\ \boxed{a_1 = - 3}[/tex]
[tex]a_n = a_1 + (n - 1) \times r \\ 222 = - 3 + (n - 1) \times 5 \\ 222 = - 3 + 5n - 5 \\ 222 = 5n - 8 \\ 5n = 230 | \div 5 \\ \boxed{ n = 46}[/tex]