Find next number in the series... 1/1...3/2 ...7/5...17/12...41/29...?

Question

Find the number that comes next in the following series:

3, 7, 12, 14, 16, 19, 21, 25, 30, 41, 45, 52, 54, 56, 59, 61, 65, 70, ?

Answer 1

Ans : 99/70

next_num = (numerator + 2 * denominator) / (numerator + denominator)

(1 + 2 * 1)   / (1 + 1)   = 3/2
(3 + 2 * 2)   / (3 + 2)   = 7/5
(7 + 2 * 5)   / (7 + 5)   = 17/12
(17 + 2 * 12) / (17 + 12) = 41/29
(41 + 2 * 29) / (41 + 29) = 99/70

Answer 2

next_num = (numerator + denominator + denominator) / (numerator + denominator)
(1+1+1) / (1+1) = 3/2
(3+2+2) / (3+2) = 7/5
(7+5+5) / (7+5) = 17/12
(17 +12+ 12) / (17+12) = 41/29
(41+29+29) / (41+29) = 99/70

Answer 3

Ans 99/70
As 1/1 , 3/2 = 2+1/1+1, 7/5= 5+2/3+2 ,
17/12= 12+5/7+5, 41/29=29+12/12+17,
So 70+29/41+29= 99/70

Answer 4

numerator of next term=2*numerator of previous term + numerator of second previous term;
denominator of next term=numerator of previous term + denominator of previous term.
ans=99/70

Answer 5

ans : 89/60

calculations of denominator : 1, (1*1+1 = 2), (2*2+1 = 5), (5*2+1 = 12), (29*2+2 = 60)

calculation of Nrd : 1/2, 3/2, 2/5, 17/12, 41/29
(1+2 = 3) i.e Numerator of 1st term + Denominator of 2nd term = Numerator of 2nd term
(2+5 = 7), (5+12 = 17), (12+29 = 41)

so the answer is 89/60

Answer 6

Answer:
99/70 is the answer