Lesson Plans SET A for Grades 9-10-Lesson 6 Level 9-10 Sequences and Patterns Homework

Lesson 6 Level 9-10 Sequences and Patterns Homework

Pdf Summary

The problem set from Lesson 6 on Sequences and Patterns offers five intriguing math challenges designed to enhance understanding of mathematical sequences and patterns, particularly for Math Kangaroo participants. Below is a summary of the problems given:<br /><br />1. **Consecutive Sum Sequence**: You are given a sequence of 2024 numbers where the sum of any three consecutive numbers is 20. It is known that the 15th number is 5 and the 151st number is 7. The goal is to determine the last number in this sequence.<br /><br />2. **Quotient Sequence**: In this sequence, the first number is 2 and the second is 3. Each subsequent number after the second is determined by the quotient of the number before last divided by the last. The task is to find the value of the eleventh number.<br /><br />3. **Odd Numbers in a Triangle**: Paul is to fill a diagram with numbers where each number is the sum of the two numbers directly beneath it. The aim is to find the maximum number of odd numbers Paul can place in this configuration.<br /><br />4. **Number Replacement on a Blackboard**: Numbers from 1 to 10 are written on a blackboard. John repeatedly removes two numbers and replaces them with a new number, which is the vector difference of the two original numbers squared. The challenge is to determine the final number left on the board after this process continues until one number remains.<br /><br />5. **Multiplicative Sum Sequence**: This sequence starts with the product of all integers from 1 to 50. Each subsequent number is the sum of the digits of the previous number, and the sequence continues until a one-digit number is reached. The question asks for this final one-digit number.<br /><br />These problems encourage critical thinking and problem-solving skills through intricate sequence and pattern challenges.

Keywords

Sequences

Patterns

Math Kangaroo

Consecutive Sum Sequence

Quotient Sequence

Odd Numbers

Number Replacement

Multiplicative Sum Sequence

Problem Solving

Mathematical Challenges