Answer:
\(a_{241} = 1\)
Step-by-step explanation:
\(a_{1}=1\\a_{2}=2\\\\a_{n}=\frac{a_{n-1}}{a_{n-2}}\\\\a_{3}=\frac{a_2}{a_1}=\frac{1}{2}\\\\a_{4}=\frac{a_3}{a_2}=\frac{\frac{1}{2}}{2}=\frac{1}{4}\\\\a_{5}=\frac{a_4}{a_3}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}\\\\a_{6}=\frac{a_5}{a_4}=\frac{\frac{1}{2}}{\frac{1}{4}}=2}\\\\a_{7}=\frac{a_6}{a_5}=\frac{\frac{1}{2}}{2}=4\\\\a_{8}=\frac{a_7}{a_6}=\frac{4}{2}=2\\\\a_{9}=\frac{a_8}{a_7}=\frac{2}{4}=\frac{1}{2}\\\\a_{10}=\frac{a_9}{a_8}=\frac{\frac{1}{2}}{2}=\frac{1}{4}\)
Now, as observed the pattern is getting repeated
\(a_3 = a_9\\a_4=a_{10}\\\therefore a_n=a_{n+6\cdot w}\thinspace ;\text{w is a whole number}\\\implies a_{241}=a_{1+6\cdot 40}\\ \implies a_{241}=a_1=1\)
\(So,a_{241}=1\)
