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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: \(-5 * -2 * 3 * -5 * -2 = 300\).

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Most popular questions from this chapter

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.

Which of the following is the digit for the sum of all of the distinct prime integers less than 20 ? A. $$4$$ B. $$5$$ C. $$6$$ D. $$7$$ E. $$8$$

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