Review question

# Given this definition of $F(n)$, can we find the value of $F(6000)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8168

## Suggestion

The function $F(n)$ is defined for all positive integers as follows; $F(1)=0$, and for all $n \geq 2$, \begin{align*} &F(n) = F(n-1) + 2 \quad\quad\quad\quad \text{if 2 divides n but 3 does not divide n};\\ &F(n) = F(n-1) + 3 \quad\quad\quad\quad \text{if 3 divides n but 2 does not divide n};\\ &F(n) = F(n-1) + 4 \quad\quad\quad\quad \text{if 2 and 3 both divide n};\\ &F(n) = F(n-1) \quad\quad\quad\quad\quad\quad \text{if neither 2 nor 3 divides n}. \end{align*}

The value of $F(6000)$ equals

$(a)\quad 9827,\quad(b)\quad 10121,\quad(c)\quad 11000,\quad(d)\quad 12300,\quad(e)\quad 12352.$

Can we use the rules to evaluate $F(n)$ for small $n$?

Can we find any pattern in the sequence given by the amounts we add on each time? Might this sequence be periodic?