2. A piece of string 42 centimeters long is cut into 2 unequal pieces. The longer
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I think you mean 
basically that measn yo divide that term by the previous term
ok
a3=a1/a2=1/2
a4=a3/a2=(1/2)/2=1/4
a5=a4/a3=(1/4)/(1/2)=1/2
a6=a5/a4=(1/2)/(1/4)=2
a7=a6/a5=2/(1/2)=4
a8=a7/a6=4/2=2
a9=a8/a7=2/4=1/2
a10=a9/a8=(1/2)/2=1/4
ok, so notice a pattern
a3=a9
a4=a10
I therefor conclude that
where w is a whole number
and n>2ok, so
241=6*39+7
so therefor
therefor the 241th term is same as a7 or 4
I say a241 is 4
basically that measn yo divide that term by the previous term
ok
a3=a1/a2=1/2
a4=a3/a2=(1/2)/2=1/4
a5=a4/a3=(1/4)/(1/2)=1/2
a6=a5/a4=(1/2)/(1/4)=2
a7=a6/a5=2/(1/2)=4
a8=a7/a6=4/2=2
a9=a8/a7=2/4=1/2
a10=a9/a8=(1/2)/2=1/4
ok, so notice a pattern
a3=a9
a4=a10
I therefor conclude that
and n>2ok, so
241=6*39+7
so therefor
therefor the 241th term is same as a7 or 4
I say a241 is 4