Question

4. The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation Fn F-1 F-2 where F F2 1 and by convention Fo 0. For example, the first 8 Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21. (a) For a given n, compute the nth Fibonnaci number using a for loop (b) For a given n, compute the nth Fibonnaci number using a while loop Print the 15th Fibonacci number obtained from each of the code written above. Hint: You can create a function taking n as argument. Alternatively, write the code for n-15

Using R code only

Answer 1

a)

for loop

len <- 15
fibvals <- numeric(len)
fibvals[1] <- 1
fibvals[2] <- 1
for (i in 3:len) { 
   fibvals[i] <- fibvals[i-1]+fibvals[i-2]
} 

fibvals

b)

while loop

Fibonacci <- function(n) {
    x <- c(0,1)
    while (length(x) < n) {
        position <- length(x)
        new <- x[position] + x[position-1]
        x <- c(x,new)
    }
    return(x)
}