Write both the explicit and recursive equations for this sequence: 7, 10, 13, 16,…. Show yourwork/explain your thinking for how you get each component of both of the equations.

Question

03-11-2022
Mathematics

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Write both the explicit and recursive equations for this sequence: 7, 10, 13, 16,…. Show yourwork/explain your thinking for how you get each component of both of the equations.

Sagot :

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CeasarS6902 CeasarS6902 · Answer 1 · 2022-11-03T23:50:09-04:00

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

[tex]undefined[/tex]

Write both the explicit and recursive equations for this sequence: 7, 10, 13, 16,…. Show yourwork/explain your thinking for how you get each component of both of the equations.

Sagot :

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