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Ställa upp en rekursiv formel

Beskriv talföljden 1,2,4,7,11,... med en rekursiv formel. Vi börjar med att försöka hitta ett mönster.

Stalla upp en rekursiv formel.svg

Vi ser att differensen mellan två intilliggande element ökar med 1 för varje steg man tar.

Element Värde Uttryck
a1 1 1
a2 2
a3 4
a4 7
a5 11
Nu ser vi i högerkolumnen att indexet är samma tal som det man adderar. Man kan därför skriva den rekursiva formeln som

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