등비수열의 곱

등비수열 $\left\{ a _{n} \right\}$의 공비를 $r$라 하면 $a _{1} a _{5} = a _{1} \times a _{1} r ^{4}$ $= a _{1} ^{2} r ^{4} = 9$$\cdots \text{㉠}$ $a _{2} a _{6} = a _{1} r \times a _{1} r ^{5}$ $= a _{1} ^{2} r ^{6} = 36$$\cdots \text{㉡}$ $\text{㉡} \div \text{㉠}$에서 $r ^{2} = 4$ ∴ $r = 2$ ($\because r > 0$) ㉠에서 $\displaystyle a _{1} ^{2} = \frac{9}{16}$ ∴ $8 ( a _{1} a _{2} + a _{3} a _{4} )$$= 8 a _{1} ^{2} ( r + r ^{2} \times r ^{3} )$ $\displaystyle = 8 \times \frac{9}{16} \times \left( 2 + 2 ^{2} \times 2 ^{3} \right)$ $\displaystyle = \frac{9}{2} \times 34$$= 153$