Question

me ajudem nesse exercício

Answer 1

vamos calcular x na P.A.

$x- \frac{2}{3} -(x-1)= \frac{2x}{3} +1-(x- \frac{2}{3} ) \\ \\ x- \frac{2}{3} -x+1= \frac{2x}{3} +1-x+\frac{2}{3} \\ \\ mmc=3 \\ \\ 3x-2-3x+3=2x+3-3x+2 \\ \\ 3x-3x-2x+3x=3+2-3+2 \\ \\ x=4$

como x=4
$a_1=x-1=4-1=3 \\ \\ a_2=x- \frac{2}{3} =4- \frac{2}{3} = \frac{12-2}{3} = \frac{10}{3}$

calcular razão
$r=a_2-a_1 \\ \\ r= \frac{10}{3} -3= \frac{10-9}{3} = \frac{1}{3}$

vamos calcular o 16° n°

$a_n=a_{16}=? \\ a_1=3 \\ n=16 \\ r= \frac{1}{3} \\ \\ a_n=a_1+(n-1)r \\ \\ a_{16}=3+(16-1)( \frac{1}{3} ) \\ \\ a_{16}=3+15( \frac{1}{3}) \\ \\ a_{16}=3+5 \\ \\ a_{16}=8 \\ \\ \\ Letra~~D$