등비수열 곱

[출제의도] 등비수열 이해하기 등비수열 $\{ a _{n} \}$의 첫째항을 $a$, 공비를 $r$라 하면 $a _{5} \times a _{6} = ar ^{4} \times ar ^{5} = a ^{2} r ^{9} = 2$ $a _{1} \times a _{2} \times a _{3} \times \cdots \times a _{10}$ $= a \times ar \times ar ^{2} \times \cdots \times ar ^{9}$ $= a ^{10} r ^{45}$$= \left( a ^{2} r ^{9} \right) ^{5}$$= 2 ^{5}$$= 32$ (별해) 등비수열 $\{ a _{n} \}$에서 $a _{1} \times a _{10}$$= a _{2} \times a _{9}$$= \cdots$$= a _{5} \times a _{6} = 2$ $a _{1} \times a _{2} \times a _{3} \times \cdots \times a _{10}$$= \left( a _{5} \times a _{6} \right) ^{5} = 2 ^{5} = 32$