SOLUTION
Step 1 :
In this question, we are meant to write the recursive formula of the sequence:
[tex]-2,\text{ 4, 10 , 16 ,}\ldots\ldots[/tex]Step 2 :
From the sequence, we have that :
[tex]\begin{gathered} a\text{ = first term = - 2} \\ _{} \end{gathered}[/tex][tex]\begin{gathered} d\text{ = common difference} \\ =T_{2\text{ }}-T_1 \\ =\text{ 4 - ( -2 )} \\ =\text{ 4 + 2 } \\ \text{= 6} \end{gathered}[/tex]Using the nth term of the sequence formula for Arithmetic Sequence,
We have that:
[tex]\begin{gathered} T_n\text{ = a + ( n- 1) d} \\ =\text{ -2 + ( n - 1) 6} \\ =\text{ -2 + 6n - 6} \\ =\text{ 6n - 8} \end{gathered}[/tex]CONCLUSION:
The recursive formula for the sequence =
[tex]T_n\text{ = 6n -8}[/tex]