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

Lesson 6 Level 9-10 Sequences and Patterns Homework Solutions

Pdf Summary

The document contains solutions to various math problems involving sequences, patterns, and properties of numbers. Here's a condensed summary:<br /><br />1. **Sequence Analysis:** The sequence consists of repeating triplets "ABC". Knowing the sequence length or mod results helps in predicting specific terms. For instance, it concludes that the 151st term is 'A'. The sum of terms A, B, and C equals 20, allowing the deduction that 'B' is 8.<br /><br />2. **Modified Fibonacci Sequence:** A sequence inspired by Fibonacci with alternating signs is analyzed. The solution seeks the 10th term, relating it to conventional Fibonacci numbers. Specifically, utilizing the sequence 1, -1, 2, -3, ..., -8 to find the term corresponding to the position.<br /><br />3. **Configuration Problem (MK 2017):** This involves maximizing the number of 'Os' in a row pattern constraint, forming a pyramid-like arrangement. Through experimentation with various configurations, it is noted that filling rows with constraints like OEOEOE leads to optimizing the total 'Os'. It concludes that a maximum of 14 'Os' can be achieved under the given conditions.<br /><br />4. **Rewrite and Simplification:** A mathematical expression simplification leads to a result irrespective of the order of operations, ending at a factorial-based expression (11!).<br /><br />5. **Multiples and Digit Sum Properties:** It discusses the divisibility principle using factorial numbers and their digit sum properties related to being a multiple of 9. Specifically, all factorials from 6! onward yield a sum of digits that equals 9, excluding 0 as an unlikely result. This result is rooted in consistent divisibility patterns observable from factorial numbers.<br /><br />These solutions present mathematical thinking around repeating patterns, sequence modifications, maximizing configurations within constraints, and understanding properties of numbers like factorials and divisibility.

Keywords

sequence analysis

repeating triplets

modified Fibonacci

pyramid configuration

factorial simplification

digit sum properties

divisibility principle

mathematical patterns

number properties

sequence prediction