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Two consecutive terms in an ARITHMETIC sequence are given. Find the recursive function.

Two Consecutive Terms In An ARITHMETIC Sequence Are Given Find The Recursive Function class=

Sagot :

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The recursive formula have the following format:

[tex]a_{n+1}=a_n+d[/tex]

Where 'd' is the common difference between each term.

From the text, we know that

[tex]\begin{gathered} a_3=5 \\ a_4=8 \end{gathered}[/tex]

Plugging those values in our formula, we find that the common difference between our terms is 3.

This gives us the following recursive function:

[tex]f(n+1)=f(n)+3[/tex]

Evaluating the function at '5' and '6', we get the following:

[tex]\begin{gathered} f(5)=f(4)+3=8+3=11 \\ f(6)=f(5)+3=11+3=14 \end{gathered}[/tex]

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