Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 6

$$-2,3,-5,-2,3,-5,-2,3,-5, \dots$$ In the sequence above, the first 3 terms repeat without end. What is the product of the 81 st term through the 85 th term?

Short Answer

Expert verified
The product of the 81st term through the 85th term of the sequence is 300

Step by step solution

01

Understand the repeating pattern

Notice that the sequence provided is a repetition of the group of numbers -2, 3, -5. This is a pattern of 3 numbers, and it repeats itself without end. Therefore, each element in the sequence can be associated with a position within this repeating 3-digit pattern.
02

Map the 81st to 85th terms within the repeating pattern

Since the pattern repeats every 3 numbers, to find the position within the 3-digit pattern for terms 81 to 85, we calculate each of these terms modulo 3. For instance, 81 modulo 3 which is 81%3 gives 0. That means the 81st term is the third number in the pattern which is -5. We continue this process to the 85th term.
03

Identify the corresponding terms

Following the process from step 2, we find that the 81st term corresponds to -5, the 82nd to -2, the 83rd to 3, the 84th to -5 again and finally, the 85th term corresponds to -2.
04

Multiply the identified terms together

Finally, to get the product of terms 81st to the 85th, we multiply together the identified terms: \(-5 * -2 * 3 * -5 * -2 = 300\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If \(x\) is the remainder when a multiple of 4 is divided by \(6,\) and \(y\) is the remainder when a multiple of 2 is divided by \(3,\) what is the greatest possible value of \(x+y ?\) A. $$2$$ B. $$3$$ C. $$5$$ D. $$6$$ E. $$9$$

If the product of two distinct integers is \(91,\) then which of the following could be the sum of the two integers? Indicate all such sums. A. $$-92$$ B. $$-91$$ C. $$7$$ D. $$13$$ E. $$20$$

During a sale, a store decreases the prices on all of its scarves by 25 to 50 percent. If all of the scarves in the store were originally priced at \(\$ 20,\) which of the following prices could be the sale price of a scarf? Indicate all such prices. A. $$\$ 8$$ B. $$\$ 10$$ C. $$\$ 12$$ D. $$\$ 14$$ E. $$\$ 16$$

Quantity \(\mathbf{A}\) The greatest number of consecutive nonnegative integers which have a sum less than 22 Quantity_B 6 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given.

Quantity_A \(4\left(\frac{1}{2} x+2 y\right)\) Quantity \(\mathbf{B}\) \(2 x+8 y\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
See all solutions

Recommended explanations on English Textbooks

5 Paragraph Essay

Read Explanation

Blog

Read Explanation

Lexis and Semantics Summary

Read Explanation

Morphology

Read Explanation

English Language Study

Read Explanation

Linguistic Terms

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free