Question

Find the first 4 terms of the recursively defined sequence. a(sub 1)=6, a(sub n+1)= 1+ (1/a(sub n)... a(sub 2)=? a(sub 3)=? a(sub 4)=?

Answer 1

This sequence is defined by giving the first term (a1 = 6), and telling you how to find any term by using the previous term ( a(n+1) = 1 + 1/a(n) ).  We already know the first term is 6.  The second term is then  a2 = 1 + 1/6 = 7/6.  The third term uses the second term.  a3 = 1 + 1/(7/6) = 13/7.  I'll leave the 4th term for you to find, but you can check your answer by confirming the 5th term is 33/20.