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The recursive rule for a sequence is shown. an=an−1+6 a1=39 What is the explicit rule for this sequence? an=33n+6 an=33n−6 an=6n−33 an=6n+33

Respuesta :

Given that, [tex] a_{1} [/tex] = 39

We will find the second term [tex] a_{2} [/tex][tex] a_{2} = a_{1} + 6 = 39 + 6 = 45 [/tex]

Similarly,

[tex] a_{3} = 45 + 6 = 51 [/tex]

Now we use the option checking method,

Suppose we check 4th option

a_{n}= 6n + 33

for n=1

[tex] a_{1} [/tex] = 6(1) + 33 = 39

[tex] a_{2} = 6(2) + 33 = 12 + 33 = 45a_{3} = 6(3) + 33 = 18 + 33 = 51 [/tex]

It means option D is correct

The explicit formula for this sequence is [tex]\rm a_n= 6n+33[/tex].

Given that

The recursive rule for a sequence is shown.

[tex]\rm a_n=a_n-1+6, \ a_1=39.[/tex]

We have to determine

What is the explicit rule for this sequence?

According to the question

The recursive rule for a sequence is shown.

[tex]\rm a_n=a_n-1+6, \ a_1=39.[/tex]

The recursive formula for a geometric sequence:

[tex]\rm a_n=a+d(n-1)[/tex]

Where a is the first term, d is a common difference, and n is the number of terms.

Then,

The second term of the sequence is given by,

[tex]a_2 = a_1 +6\\ \\ a_2 = 39+6\\ \\ a_2 = 45[/tex]

The third term of the sequence is,

[tex]\rm a_3 = a_2+1\\ \\ a_3 = 45+6\\ \\ a_3=51[/tex]

Therefore,

The explicit formula for this sequence is,

[tex]\rm a_n= 6n+33[/tex]

Hence, the explicit formula for this sequence is [tex]\rm a_n= 6n+33[/tex].

To know more about Geometric sequence click the link given below.

https://brainly.com/question/7641051

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