Question

4) Given the following Table, use the recursive method to show what the 5th term wouldbe (show all work and formulas).

Answer 1

36

Step-by-step explanation

The table represents an arithmetic sequence.

The recursive method for an arithmetic sequence is modelled by the formula:

`\begin{gathered} t_n=t_(n-1)\text{ + d} \\ \text{where t}_n\text{ = nth term} \\ t_(n-1)\text{ = (n - 1)th term} \\ d=\text{ common difference} \end{gathered}`

What this simply means is that to find the fifth term:

=> find the common difference

=> add the common difference to the fourth term

The common difference, d, is gotten by solving for the difference between two consecutive terms.

Let us pick 15 and 22. We have that:

d = 22 - 15

d = 7

The fourth term is 29, therefore, the 5th term with be:

t(5) = 29 + 7

t(5) = 36

That is the fifth term using recursive method.