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Sagot :
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sequence
[tex]7,10,13,16,...[/tex]STEP 2: Find the common difference
It can be seen that the given sequence is an arithmetic sequence, therefore, the common difference is:
[tex]\begin{gathered} d=T_2-T_1=T_3-T_2=T_4-T_3 \\ T_1=a=7 \\ T_2=10 \\ T_3=13 \\ T_4=16 \\ \\ d=10-7=13-10=16-13=3 \\ \end{gathered}[/tex]STEP 3: Get the explicit equation
Using the equation for getting the nth term of an arithmetic sequence which is given below:
[tex]T_n=a+(n-1)d[/tex]a = 7, d =3,
hence the explicit equation becomes:
[tex]\begin{gathered} T_n=7+(n-1)3 \\ T_n=7+3n-3 \\ T_n=4+3n \end{gathered}[/tex]STEP 4: Get the recursive equation
[tex]\begin{gathered} T_1=a=7 \\ T_2=T_1+d \\ T_3=T_2+d \\ T_n=T_{n-1}+d \end{gathered}[/tex]Therefore the equations are given below:
Explicit equation
[tex]T_n=4+3n[/tex]Recursive equation
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