Question 1

1 pts

Given the sequence:

25, 21, 17, 13,…

Write the explicit equation that models the sequence.

A. an

4n + 29

B. an

25 +(-4)(n-1)

C. an = -25 +(-4)(n-1)

D. an

= 4 + 25

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1 pts

Given the sequence:

25, 21, 17, 13,…

Write the explicit equation that models the sequence.

A. an

4n + 29

B. an

25 +(-4)(n-1)

C. an = -25 +(-4)(n-1)

D. an

= 4 + 25

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Answer:The correct answer is: Option B:[tex]a_n = 25+(-4)(n-1)[/tex]Step-by-step explanation:Given sequence is:

25, 21, 17, 13,…

Here

a1 = 25

a2 = 21

a3 = 17

First of all we have to determine the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence.

So,

[tex]d = a_2 – a_1 = 21-25 = -4\\d =a_3-a_2 = 17-21 = -4[/tex]

The explicit formula is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

Putting the value of a1 and d

[tex]a_n = 25 + (n-1)(-4)\\a_n = 25-4n+4\\a_n = 29-4n[/tex]

Hence,

The correct answer is: Option B:[tex]a_n = 25+(-4)(n-1)[/tex]