13th Fibonacci number

Calculating the 13th 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 (13 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

Sum of the first 13 Fibonacci numbers

SUMM = F1 + F2 + F3 + F4 + F5 + F6 + F7 + F8 + F9 + F10 + F11 + F12 + F13 = 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 = 609