등비수열 세 항씩 합

$a _{n} = ar ^{n-1}$이라 두면 $a + ar + ar ^{2} = 48 , ar ^{3} + ar ^{4} + ar ^{5} = 12 = r ^{3} ( a + ar + ar ^{2} )$ $\displaystyle \therefore r ^{3} = \frac{1}{4}$ $\displaystyle \therefore a _{7} + a _{8} + a _{9} = ar ^{6} + ar ^{7} + ar ^{8} = r ^{6} ( a + ar + ar ^{2} ) = \left( \frac{1}{4} \right) ^{2} \cdot 48 = 3$