Question

Generate the first 5 terms of this sequence:
f(1) = 2 and f(2) = 3, f(n) = f(n - 1) + f(n - 2), for n > 2.
A. 2, 3, 5, 7, 9
B. 2, 3, 4, 7, 11
C. 2, 3, 5, 9, 11
D. 2, 3, 5, 8, 13

Answer 1

Ok, so we got a fibonacci here

Answer 2

You are already given the first two terms,
\(a_1=2\)
\(a_2=3\)

I am changing my notation, mam, if you don't mind.... (do you?)

Answer 3

D

Answer 4

i dont mind and thnx zupari :)

Answer 5

You are given that:

\(\large\color{black}{ \displaystyle a_n=a_{n-1}+a_{n-2} }\)

(i.e. every Nth term is going to be equal (or given by) the sum of the 2 terms before it)

Answer 6

So, we can use this for 3rd, 4th and 5th terms

Answer 7

\(\large\color{black}{ \displaystyle a_3=a_{2}+a_{1}=3+2=5 }\)

Answer 8

\(\large\color{black}{ \displaystyle a_4=a_{3}+a_{2}=5+3=8 }\)

Answer 9

\(\large\color{black}{ \displaystyle a_5=a_{4}+a_{3}=8+5=13 }\)

Answer 10

lets look at it entirely.

\(\large\color{black}{ \displaystyle 2,~3,~5,~8,~13 }\)

Answer 11

So can see just by looking how every term (from 3rd term and on) has a value same as the sum of the 3 terms before it)