SOLUTION: 1/12, 2/13, 3/14, 4/15... is this sequence geometric, arithmetic, or neither

Algebra ->  Sequences-and-series -> SOLUTION: 1/12, 2/13, 3/14, 4/15... is this sequence geometric, arithmetic, or neither      Log On


   

Question 42189: 1/12, 2/13, 3/14, 4/15...
is this sequence geometric, arithmetic, or neither
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let us denote the first term by 't1', second term by 't2' and so on.

t2%2Ft1=%282%2F13%29%2F%281%2F12%29=24%2F13

t3%2Ft2=%283%2F14%29%2F%282%2F13%29=39%2F28

t4%2Ft3=%284%2F15%29%2F%283%2F14%29=56%2F45

So, clearly, the numbers are not in G.P. or Geometric Progression as there is no common ratio.

Again,
t2-t1=2%2F13-1%2F12=11%2F156

t3-t2=3%2F14-2%2F13=11%2F182

t4-t3=4%2F15-3%2F14=11%2F210

So, clearly, the numbers are not in A.P. or Arithmetic Progression as there is no common difference.

Hence the numbers are neither in A.P. nor in G.P.