Question

Numa PA o oitavo termo é 30 e o vigésimo termo é 60.Determine a razão da PA e seu primeiro termo.

Answer 1

$a_{20}-a_{8}=a_1+19r-(a_1+7r)=60-30\\ \\ a_1+19r-a_1-7r=30\\ \\ 12r=30\\ \\ r=\frac{30}{12}\\ \\ \boxed{r=2,5}\\ \\ a_8=a_1+7r=30\\ \\ a_1+7*2,5=30\\ \\ a_1+17,5=30\\ \\ a_1=30-17,5\\ \\ a_1=12,5$

Answer 2

$Resolu\c{c}\~ao(r) \to \left\{\begin{array}{ccc}a_n = a_1+(n-1)*r\\\\a_{20} = a_8+(20-8)*r\\\\60 = 30+12r\\\\12r = 30\\\\ \boxed{r = \frac{30}{12} = \frac{5}{2}} \end{array}\right$


$Resolu\c{c}\~ao(a_1) \to \left\{\begin{array}{ccc}a_n = a_1+(n-1)*r\\\\a_{8} = a_1+(8-1)*r\\\\30 = a_1+7* \frac{5}{2} \\\\a_1 = 30- \frac{35}{2} \\\\ \boxed{a_1 = \frac{60-35}{2} = \frac{25}{2}} \end{array}\right$

Espero ter ajudado. :))