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Find the sum of 15+21+27+......+201.

Ans : 99/70

Solution:

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

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

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

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

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: 99/70 is the answer

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, ?

Complete the series-

9 5 14 8 3 12 7 2 23 5 2 29 3 9 ??