Question

BONUS: (5 points)Write the recursive formula for the following sequence:-2,4, 10,16

Answer 1

Step 1 :

In this question, we are meant to write the recursive formula of the sequence:

`-2,\text{ 4, 10 , 16 ,}\ldots\ldots`

Step 2 :

From the sequence, we have that :

`\begin{gathered} a\text{ = first term = - 2} \\ _{} \end{gathered}`
`\begin{gathered} d\text{ = common difference} \\ =T_{2\text{ }}-T_1 \\ =\text{ 4 - ( -2 )} \\ =\text{ 4 + 2 } \\ \text{= 6} \end{gathered}`

Using the nth term of the sequence formula for Arithmetic Sequence,

We have that:

`\begin{gathered} T_n\text{ = a + ( n- 1) d} \\ =\text{ -2 + ( n - 1) 6} \\ =\text{ -2 + 6n - 6} \\ =\text{ 6n - 8} \end{gathered}`

CONCLUSION:

The recursive formula for the sequence =

`T_n\text{ = 6n -8}`