n f(n-1)+f(n-2)
0 3
1 4
2 7
3 11
4 18
5 29
6 47
7 76
8 123
9 199
10 322
11 521
12 843
13 1364
14 2207
15 3571
16 5778
17 9349
18 15127
19 24476
20 39603
21 64079
22 103682
23 167761
24 271443
25 439204

Let's now look at the ratios again for the different pairs of terms. This is really interesting because the common ratios turn out to be exactly the same as they were for the Fibonacci sequence. No matter what two numbers we choose for f(0) and f(1), the common ratios will remain the same.

n f(n-1)+f(n-2) Each pair Every other Every third Every fourth Every fifth
0 3 1.33333333333333 2.33333333333333 3.66666666666667 6 9.66666666666667
1 4 1.75 2.75 4.5 7.25 11.75
2 7 1.57142857142857 2.57142857142857 4.14285714285714 6.71428571428571 10.8571428571429
3 11 1.63636363636364 2.63636363636364 4.27272727272727 6.90909090909091 11.1818181818182
4 18 1.61111111111111 2.61111111111111 4.22222222222222 6.83333333333333 11.0555555555556
5 29 1.62068965517241 2.62068965517241 4.24137931034483 6.86206896551724 11.1034482758621
6 47 1.61702127659574 2.61702127659574 4.23404255319149 6.85106382978723 11.0851063829787
7 76 1.61842105263158 2.61842105263158 4.23684210526316 6.85526315789474 11.0921052631579
8 123 1.61788617886179 2.61788617886179 4.23577235772358 6.85365853658537 11.0894308943089
9 199 1.61809045226131 2.61809045226131 4.23618090452261 6.85427135678392 11.0904522613065
10 322 1.61801242236025 2.61801242236025 4.2360248447205 6.85403726708075 11.0900621118012
11 521 1.61804222648752 2.61804222648752 4.23608445297505 6.85412667946257 11.0902111324376
12 843 1.61803084223013 2.61803084223013 4.23606168446026 6.85409252669039 11.0901542111507
13 1364 1.61803519061584 2.61803519061584 4.23607038123167 6.85410557184751 11.0901759530792
14 2207 1.6180335296783 2.6180335296783 4.23606705935659 6.85410058903489 11.0901676483915
15 3571 1.61803416409969 2.61803416409969 4.23606832819938 6.85410249229908 11.0901708204985
16 5778 1.61803392177224 2.61803392177224 4.23606784354448 6.85410176531672 11.0901696088612
17 9349 1.61803401433308 2.61803401433308 4.23606802866617 6.85410204299925 11.0901700716654
18 15127 1.61803397897799 2.61803397897799 4.23606795795597 6.85410193693396 11.0901698948899
19 24476 1.61803399248243 2.61803399248243 4.23606798496486 6.8541019774473 11.0901699624122
20 39603 1.61803398732419 2.61803398732419 4.23606797464839 6.85410196197258 11.090169936621
21 64079 1.61803398929446 2.61803398929446 4.23606797858893 6.85410196788339
22 103682 1.61803398854189 2.61803398854189 4.23606797708378
23 167761 1.61803398882935 2.61803398882935
24 271443 1.61803398871955
25 439204

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