등비수열의 항

등비수열 $\left\{ a _{n} \right\}$의 첫째항을 $a \left( a > 0 \right)$, 공비를 $r \left( r > 0 \right)$이라 하자. $a _{n} = ar ^{n - 1}$ (단, $n$은 자연수) $a _{1} + a _{2} = a + ar$ $a _{3} + a _{4} = ar ^{2} + ar ^{3} = r ^{2} \left( a + ar \right)$ $\displaystyle \frac{a _{3} + a _{4}}{a _{1} + a _{2}} = \frac{r ^{2} \left( a + ar \right)}{a + ar} = r ^{2} = 4$, $r = 2 \left( r > 0 \right)$ $a _{2} a _{4} = a ^{2} r ^{4} = 16 a ^{2} = 1$, $\displaystyle a = \frac{1}{4} \left( a > 0 \right)$ $\displaystyle a _{n} = \frac{1}{4} \times 2 ^{n - 1}$, $a _{6} = 8$, $a _{7} = 16$ 따라서 $a _{6} + a _{7} = 24$