Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

47

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 816

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Find each sum
$4 + 4.5 + 5 + 5.5 + . . . + 100$

The solution is $S_{193} = 10036$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

$4 + 4.5 + 5 + 5.5 + . . . + 100$

Step 2: Calculation

We have, $4 + 4.5 + 5 + 5.5 + . . . + 100$

So, $a_{1} = 4, d = 0.5, a_{n} = 100$

Now use formula,

$a_{n} = a_{1} + (n - 1) d \Rightarrow 100 = 4 + (n - 1) 0.5 \Rightarrow 100 = 4 + 0.5 n - 0.5 \Rightarrow 0.5 n = 96.5 \Rightarrow n = 193$

To find sum $S_{193}$

$S_{193} = \frac{193}{2} [4 + 100] = 10036$

Most popular questions for Math Textbooks

In Problems 51–60, write out each sum.

$\sum_{k = 1}^{n} {(k + 1)}^{2}$

In Problems 61–70, express each sum using summation notation.

$1^{3} + 2^{3} + 3^{3} + . . . . + 8^{3}$

Fibonacci Sequence: Let

$u_{n} = \frac{{(1 + \sqrt{5})}^{n} - {(1 - \sqrt{5})}^{n}}{2^{n} \sqrt{5}}$

define the nth term of a sequence.

(a) Show that u₁= 1 and u₂ = 1.

(b) Show that u_n+2 = u_n+1 + u_n.

(c) Draw the conclusion that {u_n} is the Fibonacci sequence.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = A; a_{n} = a_{n - 1} + d$

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$\sum_{k = 1}^{\infty} \frac{1}{2} 3^{k - 1}$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free