Question

Consider the sequence 1, 2/3, 3/5, 4/7, 5/9 .
a.Describe the pattern formed in the sequence.
b. Find the next three terms.

Answer 1

note that the numerators are 1,2,3,4,5
and denominators are 1,3,5,7,9

Answer 2

both these are arithmetic sequences

Answer 3

numerators have first term 1 and common difference 1
denominator have first term 1 and common difference 2

nth term can be written as n / (1 + 2(n- 1))

Answer 4

the next 3 terms are 6/11, 7/13 and 8/15.

Answer 5

simplifying the nth term gives n / (2n-1)