What are the first five terms of the following sequence? a₁ = 25, an an-1-5 O 5, 10, 15, 20, 25 0 25.5.1/3-2/5 O 25, 20, 15, 10, 5 O 25, 30, 35, 40, 45
What are the first five terms of the following sequence? a₁ = 25, an an-1-5 O 5, 10, 15, 20, 25 0 25.5.1/3-2/5 O 25, 20, 15, 10, 5 O 25, 30, 35, 40, 45
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 7CT
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![**Question:**
What are the first five terms of the following sequence?
Given:
\[ a_1 = 25 \]
\[ a_n = a_{n-1} - 5 \]
**Options:**
A.
\[ 5, 10, 15, 20, 25 \]
B.
\[ 25, 5, \frac{1}{5}, \frac{1}{25} \]
C.
\[ 25, 20, 15, 10, 5 \]
D.
\[ 25, 30, 35, 40, 45 \]
---
### Solution Explanation:
To determine the first five terms of the given sequence, let's calculate the terms step-by-step using the provided recursive formula:
\[ a_1 = 25 \]
\[ a_n = a_{n-1} - 5 \]
Starting with:
\[ a_1 = 25 \]
Next term:
\[ a_2 = a_1 - 5 = 25 - 5 = 20 \]
Next term:
\[ a_3 = a_2 - 5 = 20 - 5 = 15 \]
Next term:
\[ a_4 = a_3 - 5 = 15 - 5 = 10 \]
Next term:
\[ a_5 = a_4 - 5 = 10 - 5 = 5 \]
So the first five terms of the sequence are:
\[ 25, 20, 15, 10, 5 \]
Therefore, the correct option is:
C.
\[ 25, 20, 15, 10, 5 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b617bc-0d34-47a7-bf50-98a510ba10e9%2Fcf6af786-5176-4e71-a42c-d51a33fd265d%2Fla9ke7d_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
What are the first five terms of the following sequence?
Given:
\[ a_1 = 25 \]
\[ a_n = a_{n-1} - 5 \]
**Options:**
A.
\[ 5, 10, 15, 20, 25 \]
B.
\[ 25, 5, \frac{1}{5}, \frac{1}{25} \]
C.
\[ 25, 20, 15, 10, 5 \]
D.
\[ 25, 30, 35, 40, 45 \]
---
### Solution Explanation:
To determine the first five terms of the given sequence, let's calculate the terms step-by-step using the provided recursive formula:
\[ a_1 = 25 \]
\[ a_n = a_{n-1} - 5 \]
Starting with:
\[ a_1 = 25 \]
Next term:
\[ a_2 = a_1 - 5 = 25 - 5 = 20 \]
Next term:
\[ a_3 = a_2 - 5 = 20 - 5 = 15 \]
Next term:
\[ a_4 = a_3 - 5 = 15 - 5 = 10 \]
Next term:
\[ a_5 = a_4 - 5 = 10 - 5 = 5 \]
So the first five terms of the sequence are:
\[ 25, 20, 15, 10, 5 \]
Therefore, the correct option is:
C.
\[ 25, 20, 15, 10, 5 \]
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