Textbook Question
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.
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 17
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a1 = 7, d = 5.
Verified step by step guidance1
Identify the given information: the first term \(a_1 = 7\) and the common difference \(d = 5\).
Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
Substitute \(n = 50\) into the formula to find the 50th term: \(a_{50} = 7 + (50 - 1) \times 5\).
Simplify the expression inside the parentheses: calculate \(50 - 1\).
Multiply the result by the common difference \(5\) and then add the first term \(7\) to find \(a_{50}\).
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 constant is called the common difference, denoted by d. Understanding this helps identify the pattern and predict any term in the sequence.
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. Knowing d allows you to calculate any term in the sequence using the formula for the nth term.
Recommended video:
5:57Graphs of Common Functions
Formula for the nth Term of an Arithmetic Sequence
The nth term (a_n) of an arithmetic sequence is given by a_n = a₁ + (n - 1)d, where a₁ is the first term, d is the common difference, and n is the term number. This formula is essential for finding specific terms like a₅₀ without listing all previous terms.
Recommended video:
Guided course
5:17Arithmetic Sequences - General Formula
Related Practice
Textbook Question
Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence. 3, 12, 48, 192, ...
Textbook Question
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.
Textbook Question
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a1=4 and an=2an-1 + 3 for n≥2
6
views
Textbook Question
Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x²+2y)4
Textbook Question
In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. an = n2/n!