Homework Help is Here – Start Your Trial Now!
Math
Calculus
Construct a difference table to predict the next term of the sequence 10, 6, 8, 16, 30,.... A) -2 B) 50 C) 46 D) 44 E) 6

Construct a difference table to predict the next term of the sequence 10, 6, 8, 16, 30,.... A) -2 B) 50 C) 46 D) 44 E) 6

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
**Problem:** Construct a difference table to predict the next term of the sequence 10, 6, 8, 16, 30, … **Options:** A) -2 B) 50 C) 46 D) 44 E) 6 **Explanation:** To solve this problem, we need to analyze the sequence using a method called the difference table. This involves calculating the differences between consecutive terms of the sequence and continuing this process with each new set of differences until a pattern emerges. Once the differences reach a constant value, we can predict the next term. 1. **Find the first differences:** - 6 - 10 = -4 - 8 - 6 = 2 - 16 - 8 = 8 - 30 - 16 = 14 First differences: -4, 2, 8, 14 2. **Find the second differences:** - 2 - (-4) = 6 - 8 - 2 = 6 - 14 - 8 = 6 Second differences: 6, 6, 6 Since the second differences are constant, the sequence involves a quadratic pattern. We can use these differences to predict the next term. 3. **Predict the next first difference:** - Next first difference = Last first difference + Constant second difference - Next first difference = 14 + 6 = 20 4. **Predict the next term:** - Next term = Last term of the sequence + Next first difference - Next term = 30 + 20 = 50 Therefore, the next term in the sequence is 50. The answer is **B) 50**.
Transcribed Image Text:**Problem:** Construct a difference table to predict the next term of the sequence 10, 6, 8, 16, 30, … **Options:** A) -2 B) 50 C) 46 D) 44 E) 6 **Explanation:** To solve this problem, we need to analyze the sequence using a method called the difference table. This involves calculating the differences between consecutive terms of the sequence and continuing this process with each new set of differences until a pattern emerges. Once the differences reach a constant value, we can predict the next term. 1. **Find the first differences:** - 6 - 10 = -4 - 8 - 6 = 2 - 16 - 8 = 8 - 30 - 16 = 14 First differences: -4, 2, 8, 14 2. **Find the second differences:** - 2 - (-4) = 6 - 8 - 2 = 6 - 14 - 8 = 6 Second differences: 6, 6, 6 Since the second differences are constant, the sequence involves a quadratic pattern. We can use these differences to predict the next term. 3. **Predict the next first difference:** - Next first difference = Last first difference + Constant second difference - Next first difference = 14 + 6 = 20 4. **Predict the next term:** - Next term = Last term of the sequence + Next first difference - Next term = 30 + 20 = 50 Therefore, the next term in the sequence is 50. The answer is **B) 50**.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS