25th Fibonacci number

Calculating the 25th 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 (25 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

Sum of the first 25 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 = 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 = 196417