Textbook Question
Write the first five terms of each geometric sequence. an = - 4a(n-1), a1 = 10
1
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 5
Write the first six terms of each arithmetic sequence. a1 = 300, d= -90
Verified step by step guidance1
Identify the first term \(a_1\) and the common difference \(d\) of the arithmetic sequence. Here, \(a_1 = 300\) and \(d = -90\).
Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = 300 + (2 - 1) \times (-90)\).
Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = 300 + (3 - 1) \times (-90)\).
Continue this process to find the fourth, fifth, and sixth terms by substituting \(n=4, 5, 6\) respectively into the formula.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arithmetic Sequence
An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This difference is called the common difference, and the sequence progresses linearly.
Recommended video:
Guided course
5:17
Arithmetic Sequences - General Formula
Common Difference (d)
The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero, affecting whether the sequence increases, decreases, or remains constant.
Recommended video:
5:57Graphs of Common Functions
Finding Terms of an Arithmetic Sequence
To find any term in an arithmetic sequence, use the formula a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number. This formula helps generate terms without listing all previous ones.
Recommended video:
Guided course
5:17Arithmetic Sequences - General Formula
Related Practice
Textbook Question
A statement Sn about the positive integers is given. Write statements Sk and Sk+1 simplifying statement Sk+1 completely. Sn: 4 + 8 + 12 + ... + 4n = 2n(n + 1)
2
views
Textbook Question
A statement Sn about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 3 is a factor of n3 - n.
Textbook Question
Evaluate the given binomial coefficient.
Textbook Question
Write the first four terms of each sequence whose general term is given. an=(−3)n
2
views
Textbook Question
Use the formula for nPr to evaluate each expression. 6P6