Question

Determine a razão das PAs em que:
A - a7= -49 e a1=-73
B - a2= -7 e a8=17

Answer 1

$a_n=a_1+(n-1)\times r\\\\\\\\ a)~~a_7=-49~~;~~a_1=-73~~;~~n=7\\\\\\ -49 = -73 +(7-1)\times r\to\\ -49 = -73 +(7-1)\times r\to\\ -49 = -73+ 6r\to\\ -49 + 73 = 6r\to\\ 24 = 6r\to\\ \dfrac{24}{6} =r\to\\ \boxed{r=4}$




$B)~~a_2=-7~~;~~a_8=17~~;~~n=7\\\\17 = -7+(7-1)\times r\to\\ 17 = -7+6 r\to\\ 17+7=6r\to\\24 = 6r\to\\ \dfrac{24}{6} =r\to\\ \boxed{r=4} \\\\\\zzz$

Answer 2

a)
$a_1 = -73 \\ a_7 = -49 \\ r =\, ? \\ \\ a_n = a_1+(n-1)r \\ a_7 = a_1 + (7-1)r \\ a_7 = a_1 + 6r \\ \\ -49 = -73+ 6r \\ 6r = -49+73 \\ 6r = 24 \\ r = \frac{24}{6} \\ \\ r = 4$

b)
$a_2 = -7 \\ a_8 = 17 \\ r = \,? \\ \\ a_8 = a_2+(8-2)r \\ a_8 = a_2 + 6r \\ \\ 17 = -7 + 6r \\ 6r = 17+7 \\ 6r = 24 \\ r = \frac{24}{6} \\ \\ r = 4$