Explanation Given: The sequence is a n + 1 = 1 2 a n +3 and a 0 = 1000 (1) Calculation: Obtain the ten terms of the sequence. Substitute 0 for n in equation (1), a 0 + 1 = 1 2 a 0 + 3 = 1 2 1000 + 3 [ ∵ a 0 = 1000 ] ≈ 15.811 + 3 = 18.811 Therefore the second term of the sequence is, a 1 ≈ 18.811 . Substitute 1 for n in equation (1), a 1 + 1 = 1 2 a 1 + 3 ≈ 1 2 18.811 + 3 [ ∵ a 1 ≈ 18.811 ] ≈ 2.1686 + 3 = 5.1686 Therefore, the third term of the sequence is, a 2 ≈ 5.1686 . Substitute 2 for n in equation (1), a 2 + 1 = 1 2 a 2 + 3 = 1 2 5.1686 + 3 [ ∵ a 2 ≈ 5.1686 ] ≈ 1.1367 + 3 = 4.1367 Therefore, the fourth term of the sequence is, a 3 = 4.1367 . Substitute 3 for n in equation (1), a 3 + 1 = 1 2 a 3 + 3 ≈ 1 2 4.1367 + 3 [ ∵ a 3 ≈ 4.1367 ] ≈ 1.0169 + 3 = 4.0169 Therefore, the fifth term of the sequence is, a 4 ≈ 4.0169 . Substitute 4 for n in equation (1). a 4 + 1 = 1 2 a 4 + 3 ≈ 1 2 4.0169 + 3 [ ∵ a 4 ≈ 4.0169 ] ≈ 1.0021 + 3 = 4.0021 Thus, the sixth term of the sequence is a 5 ≈ 4.0021 . Substitute 5 for n in equation (1), a 5 + 1 = 1 2 a 5 + 3 ≈ 1 2 4

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 8.1, Problem 53E

To determine

A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.1, Problem 52E

Chapter 8.1, Problem 54E

Students have asked these similar questions

Solve the recurrence relations below. Fill in the blanks for the closed form expression and rate of growth. f1, T(n) = {T(n-2 if n < 2. T(n-2) 2. in 2. Assume n is always even. Closed form expression: Rate of Growth: (

Solve the following recurrence relation, using back substitution. x(n) = x(n-1) + 10 for n > 0, x(0) = 1

Consider the following recurrence relation: S T(n) = T(n – 1) +n +62 otherwise n = 1 Solve the recurrence relation by use of the substitution method. You do not need to prove your final result. Express your final result in Big-Oh notation.

Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

Solution Summary: The author explains how the sequence converges to 4. Substitute 0 for n in equation (1), c

Concept explainers

Videos

A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

Want to see the full answer?

Chapter 8 Solutions