[tex] > resolucao \\ \\ \geqslant progressao \: aritmetica \\ \\ \geqslant \: a \: razao \: da \: pa \\ \\ an = a1 + (n - 1)r \\ 83 = 43 + (10 - 1)r \\ 83 = 43 + 9r \\ 83 - 43 = 9r \\ 40 = 9r \\ r = \frac{40}{9} \\ \\ = = = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ \geqslant o \: trigessimo \: primeiro \: termo \: da \: pa \\ \\ \\ an = a1 + (n - 1)r \\ an = 43 + (31 - 1) \frac{40}{9} \\ an = 43 + 30 \times \frac{40}{9} \\ an = 43 + \frac{1200}{9} \\ an = \frac{387 + 1200}{9} \\ an = \frac{1587}{9} \\ an = \frac{529}{3} \\ \\ \\ > < > < > < > < > < > > [/tex]
