Explanation Formula used: The nth term of a Geometric Sequence: “If a geometric sequence { a n } has first term a 1 and common ratio r , then the n th term is determined by the formula a n = a 1 r n − 1 r ≠ 0 .” Sum of the first n terms of a Geometric Sequence: “Let { a n } be a geometric sequence with first term a 1 and common ratio r , where r ≠ 0 , r ≠ 1 . The sum S n of the first n terms of { a n } is S n = a 1 ⋅ 1 − r n 1 − r where r ≠ 0 , r ≠ 1 .” Calculation: To find the given sum, ∑ n = 1 8 [ 4 2 n − 1 ] . The sequence { a n } = { 4 2 n − 1 } can be written in a standard form of geometric sequence as follows. { a n } = { 4 2 n − 1 } = { 4 ⋅ ( 1 2 ) n − 1 } Thus, the sum becomes, ∑ n = 1 8 [ 4 2 n − 1 ]

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 13.3, Problem 47E

To determine

To find: The sum of the first 8 terms of a sequence 42n−1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 46E

Chapter 13.3, Problem 48E

Students have asked these similar questions

How much is the circumference of a circle whose diameter is 7 feet?C =π d

How to solve 2542/64.132

Assume that you fancy polynomial splines, while you actually need ƒ(t) = e²/3 – 1 for t€ [−1, 1]. See the figure for a plot of f(t). Your goal is to approximate f(t) with an inter- polating polynomial spline of degree d that is given as sa(t) = • Σk=0 Pd,k bd,k(t) so that sd(tk) = = Pd,k for tk = −1 + 2 (given d > 0) with basis functions bd,k(t) = Σi±0 Cd,k,i = • The special case of d 0 is trivial: the only basis function b0,0 (t) is constant 1 and so(t) is thus constant po,0 for all t = [−1, 1]. ...9 The d+1 basis functions bd,k (t) form a ba- sis Bd {ba,o(t), ba,1(t), bd,d(t)} of the function space of all possible sα (t) functions. Clearly, you wish to find out, which of them given a particular maximal degree d is the best-possible approximation of f(t) in the least- squares sense. _ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 function f(t) = exp((2t)/3) - 1 to project -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5…

Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

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

The sum of the first 8 terms of a sequence 4 2 n − 1 .

Solution Summary: The author explains that the sum of the first 8 terms of a sequence 42n-1 is 7.96875.

Videos

To find: The sum of the first 8 terms of a sequence 42n−1.

Want to see the full answer?

Chapter 13 Solutions