Textbook Question
Evaluate the given binomial coefficient.
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 7
Write the first five terms of each geometric sequence. an = - 5a(n-1), a1 = - 6
Verified step by step guidance1
Identify the first term of the geometric sequence, which is given as \(a_1 = -6\).
Recognize the recursive formula for the sequence: \(a_n = -5a_{n-1}\), meaning each term is obtained by multiplying the previous term by \(-5\).
Calculate the second term by multiplying the first term by \(-5\): \(a_2 = -5 \times a_1\).
Find the third term by multiplying the second term by \(-5\): \(a_3 = -5 \times a_2\).
Continue this process to find the fourth and fifth terms: \(a_4 = -5 \times a_3\) and \(a_5 = -5 \times a_4\).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Geometric Sequence Definition
A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. This ratio determines how the sequence progresses, either growing or shrinking exponentially.
Recommended video:
Guided course
4:18
Geometric Sequences - Recursive Formula
Recursive Formula for Sequences
A recursive formula defines each term of a sequence based on the previous term(s). In this problem, the term a_n depends on a_(n-1) multiplied by -5, which means each term is generated by applying this rule starting from the initial term.
Recommended video:
Guided course
6:40Arithmetic Sequences - Recursive Formula
Calculating Terms of a Sequence
To find terms in a sequence using a recursive formula, start with the given first term and repeatedly apply the formula to find subsequent terms. For example, multiply the first term by the common ratio to get the second term, then continue this process to find the next terms.
Recommended video:
Guided course
8:22Introduction to Sequences
Related Practice
Textbook Question
Write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2
Textbook Question
A statement Sn about the positive integers is given. Write statements Sk and Sk+1 simplifying statement Sk+1 completely. Sn: 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)
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
Evaluate the given binomial coefficient.
Textbook Question
Use the formula for nPr to evaluate each expression. 6P6