31st Fibonacci number
Calculating the 31st Fibonacci number without a calculator or programming language can be quite tedious due to the large numbers involved. However, if you're up for the challenge, you can use a method called "iterative Fibonacci sequence generation" which involves systematically generating each Fibonacci number in sequence until you reach the desired index.
Here's how you can do it manually:
Start with two variables initialized to the first two Fibonacci numbers: F0 = 0 and F1 = 1.
Continue generating Fibonacci numbers iteratively until you reach the desired index (31 in this case). The next Fibonacci number in the sequence is the sum of the previous two Fibonacci numbers.
F2 = F1 + F0 = 1 + 0 = 1
F3 = F2 + F1 = 1 + 1 = 2
F4 = F3 + F2 = 2 + 1 = 3
F5 = F4 + F3 = 3 + 2 = 5
F6 = F5 + F4 = 5 + 3 = 8
F7 = F6 + F5 = 8 + 5 = 13
F8 = F7 + F6 = 13 + 8 = 21
F9 = F8 + F7 = 21 + 13 = 34
F10 = F9 + F8 = 34 + 21 = 55
F11 = F10 + F9 = 55 + 34 = 89
F12 = F11 + F10 = 89 + 55 = 144
F13 = F12 + F11 = 144 + 89 = 233
F14 = F13 + F12 = 233 + 144 = 377
F15 = F14 + F13 = 377 + 233 = 610
F16 = F15 + F14 = 610 + 377 = 987
F17 = F16 + F15 = 987 + 610 = 1597
F18 = F17 + F16 = 1597 + 987 = 2584
F19 = F18 + F17 = 2584 + 1597 = 4181
F20 = F19 + F18 = 4181 + 2584 = 6765
F21 = F20 + F19 = 6765 + 4181 = 10946
F22 = F21 + F20 = 10946 + 6765 = 17711
F23 = F22 + F21 = 17711 + 10946 = 28657
F24 = F23 + F22 = 28657 + 17711 = 46368
F25 = F24 + F23 = 46368 + 28657 = 75025
F26 = F25 + F24 = 75025 + 46368 = 121393
F27 = F26 + F25 = 121393 + 75025 = 196418
F28 = F27 + F26 = 196418 + 121393 = 317811
F29 = F28 + F27 = 317811 + 196418 = 514229
F30 = F29 + F28 = 514229 + 317811 = 832040
F31 = F30 + F29 = 832040 + 514229 = 1346269
Sum of the first 31 Fibonacci numbers
SUMM = F1 + F2 + F3 + F4 + F5 + F6 + F7 + F8 + F9 + F10 + F11 + F12 + F13 + F14 + F15 + F16 + F17 + F18 + F19 + F20 + F21 + F22 + F23 + F24 + F25 + F26 + F27 + F28 + F29 + F30 + F31 = 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610 + 987 + 1597 + 2584 + 4181 + 6765 + 10946 + 17711 + 28657 + 46368 + 75025 + 121393 + 196418 + 317811 + 514229 + 832040 + 1346269 = 3524577