The answer to this question is simple, you start by finding 2 numbers which add up to 15 for eg 1+14 2+13 etc a good number to choose is 8 (8+7)then you would find the last number (7) then make it add up to the next number which is 20.
20-7=13 so the next number would be 13 the sequence is now 8,7,13. you would then have to make 13 add up to 23 (13-23=10)the sequence is now 8,7,13,10 the next number which is required is 16 (10+?=)?=6 the sequence is now8,7,13,10,6
the next number which is needed is 18 (6+12)12 is the next number the sequence is now 8,7,13,10,6,12 the final step is having to subtract 12 from 21 which is of course 9.
15 20
1+14 5+15
2+13 6+14
3+12 7+13<-- a common factor
4+11 8+12
5+10 9+11<-- a common factor
6+9<-- a common factor
7+8
8+7<-- a common factor
9+6
10+5
11+4
12+3
13+2
14+1
this is an example of trial and error method and this helped us find the solution. from this we can see that there is a sequence of +2 -2 in both solutions.
ANSWER=6,9,11,12,4,14,7
ANSWER=8,7,13,10,6,12,9