Whats the missing term in the geometric sequence 25, __, 225?

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Answer 1 · 2015-11-13T16:51:32

Depending on the common ratio ( $r = +-3$ ), either $A_2 = 75$ or $A_2 = -75$ .

$A_1 = 25$

$A_3 = 225$

$A_n = A_1r^(n - 1)$

$=> A_3 = A_1r^(3 - 1)$

$=> 225 = 25r^2$

$=> 9 = r^2$

$=> r = -3, r = 3$

If $r = -3$

$A_2 = 25(-3)^(2-1)$

$=> A_2 = 25(-3)$

$=> A_2 = -75$

If $r = 3$

$A_2 = 25(3)^(2-1)$
$=> A_2 = 25(3)$

$=> A_2 = 75$