contestada

The explicit rule for a sequence is given. an=3n+1 What is the recursive rule for the sequence?

a1=4; an=an−1+1

a1=3; an=an−1+1

a1=1; an=an−1+3

a1=4; an=an−1+3

Respuesta :

wegnerkolmp2741o

Answer:

a1 =4

an = an-1 +3

Step-by-step explanation:

an = 3n+1

The common difference is the coefficient on the n term

d = 3

We will add 3 each time

an = an-1 +3

Let n =1

The 1st term is

a1 = 3(1) +1

a1 =4

isyllus

Answer:

[tex]a_1=4[/tex]

Recursive Rule: [tex]a_n=a_{n-1}+3[/tex]

D is correct

Step-by-step explanation:

We are given explicit rule,

[tex]a_n=3n+1[/tex]

Put n=1

[tex]a_1=3(1)+1=4[/tex]

Now, we will find recursive rule

Put n=n-1

[tex]a_{n-1}=3(n-1)+1[/tex]

[tex]a_{n-1}=3n-2[/tex]

[tex]a_n=3n+1[/tex]

Subtract the equation

[tex]a_n-a_{n-1}=3n+1-3n+2[/tex]

[tex]a_n-a_{n-1}=3[/tex]

[tex]a_n=a_{n-1}+3[/tex]

Hence, The recursive rule is [tex]a_n=a_{n-1}+3[/tex]

Otras preguntas