Question

The terms in a sequence can be found using the recursive rule f(n)=f(n-1)-2. Find the first four terms

Answer 1

To solve for the missing numbers in the first four terms:

A recursive rule gives the first term or terms of a sequence and describes how each term is related to the preceding term(s) with a recursive equation. For example, arithmetic and geometric sequences can be described recursively.

Recursive formulas give us two pieces of information:

The first term of the sequence

The pattern rule to get any term from the term that comes before it

In the formula, n is any term number and f(n)=f(n-1) - 2

`\begin{gathered} f(n)=f(n-1)-2= \\ 3,--,\text{ -1, --} \\ \text{The first term is 3} \\ f(1)\Longrightarrow\text{ 3} \\ f(2)\Longrightarrow f(2-1)-2=f(1)-2=3-2=1 \\ f(3)\Longrightarrow f(3-1)-2=f(2)-2=1-2=-1 \\ f(4)\Longrightarrow f(4-1)-2=f(3)-2=-1-2=-3 \end{gathered}`
`3,\text{ 1, -1 , -3}`

Hence the missing number are 1 , -3