Question

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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Answer 1

Answer:

The correct answer is: Option B: $a_n = 25+(-4)(n-1)$

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,

$d = a_2 - a_1 = 21-25 = -4\\d =a_3-a_2 = 17-21 = -4$

The explicit formula is given by:

$a_n = a_1 + (n-1)d$

Putting the value of a1 and d

$a_n = 25 + (n-1)(-4)\\a_n = 25-4n+4\\a_n = 29-4n$

Hence,

The correct answer is: Option B: $a_n = 25+(-4)(n-1)$