The First Term Of A Sequence Is 24. The Rule For Generating The Sequence Is To Add 4 To Each Term. Mandy Claims That No Number In This Sequence Is A Multiple Of 5. Part A) Asks Us To Show That Mandy Is Wrong By Finding The First Number In The Sequence That Is A Multiple Of 5.

In the realm of mathematics, sequences hold a captivating allure, and in this article, we embark on a journey to unravel the intricacies of a particular sequence. We are presented with a sequence where the first term is 24, and the governing rule is deceptively simple: "add 4." This seemingly straightforward instruction gives rise to a fascinating progression of numbers. However, amidst this numerical dance, a claim emerges from Mandy, casting a shadow of doubt on the sequence's compatibility with the 5 times table. Mandy confidently asserts, "No number in this sequence is in the 5 times table." This bold statement becomes the central focus of our exploration, prompting us to meticulously examine the sequence and determine whether Mandy's conviction holds true.

At the heart of our investigation lies a sequence of numbers, a numerical tapestry woven together by a specific pattern. The sequence's origin is clearly defined: the first term proudly stands as 24. This initial value serves as the cornerstone upon which the entire sequence is constructed. The rule that dictates the sequence's progression is equally concise and elegant: "add 4." This seemingly simple instruction acts as the engine that drives the sequence forward, each term building upon its predecessor by the addition of 4. To fully grasp the sequence's behavior, we must delve deeper into its implications. The rule of "add 4" implies that the sequence will steadily ascend, with each term exceeding its predecessor by a consistent margin. This linear progression makes the sequence amenable to analysis and prediction. We can anticipate that the terms will gradually grow larger, stretching towards infinity. However, the question remains: does this continuous ascent ever intersect with the realm of multiples of 5? This is the challenge posed by Mandy's claim, and it is this question that we seek to address.

Mandy, a keen observer of numerical patterns, introduces an intriguing twist to our exploration. She confidently proclaims, "No number in this sequence is in the 5 times table." This assertion serves as a challenge, a gauntlet thrown down before the sequence itself. Mandy's statement implies a fundamental incompatibility between the sequence's inherent structure and the realm of multiples of 5. To evaluate the validity of Mandy's claim, we must first understand what it means for a number to be "in the 5 times table." A number belongs to the 5 times table if it is perfectly divisible by 5, leaving no remainder. In other words, if we divide a number by 5 and obtain a whole number as the result, then that number is a multiple of 5. With this understanding in mind, we can begin to scrutinize the sequence and determine whether any of its terms satisfy this criterion. If we encounter a number within the sequence that is indeed a multiple of 5, then Mandy's claim will be proven false. Conversely, if we exhaustively examine the sequence and fail to find any such number, then Mandy's assertion will gain credence.

To rigorously test Mandy's claim, we must embark on a quest to find a counterexample, a number within the sequence that defies her assertion. We begin by meticulously generating the initial terms of the sequence, following the prescribed rule of "add 4." Starting with the first term, 24, we successively add 4 to obtain the subsequent terms. The sequence unfolds before us: 24, 28, 32, 36, 40... As we progress through the sequence, our eyes are peeled for any number that might be a multiple of 5. The first few terms, 24, 28, 32, and 36, do not appear to satisfy this condition. However, as we reach the fifth term, a glimmer of hope emerges. The number 40 presents itself, and we must subject it to the test of divisibility by 5. Dividing 40 by 5 yields the whole number 8, confirming that 40 is indeed a multiple of 5. This discovery serves as a decisive counterexample to Mandy's claim. We have successfully identified a number within the sequence that belongs to the 5 times table, thereby disproving her assertion. Mandy's claim, though seemingly plausible at first glance, crumbles under the weight of mathematical evidence.

The evidence is irrefutable. We have unearthed a number within the sequence, 40, that proudly resides within the 5 times table. This single counterexample serves as a resounding refutation of Mandy's claim. Her assertion that "No number in this sequence is in the 5 times table" is demonstrably false. The sequence, governed by the simple rule of "add 4," does indeed intersect with the realm of multiples of 5. This revelation highlights the importance of rigorous testing and the potential for unexpected patterns to emerge within mathematical constructs. Mandy's claim, though initially compelling, ultimately falls prey to the power of mathematical scrutiny. The sequence, in its unassuming progression, holds a hidden surprise, a testament to the beauty and complexity that can be found within even the simplest of mathematical systems.

Having successfully debunked Mandy's claim, we can now shift our focus to a more specific question: What is the first number in the sequence that is in the 5 times table? Our previous exploration has already provided us with the answer. We discovered that the fifth term of the sequence, 40, is a multiple of 5. Therefore, 40 is indeed the first number in the sequence that satisfies this condition. This finding reinforces the notion that mathematical sequences, even those governed by simple rules, can exhibit unexpected patterns and intersections. The discovery of 40 as the first multiple of 5 within the sequence provides a concrete example of this phenomenon. It also underscores the importance of systematic investigation and the power of direct calculation in unraveling mathematical mysteries.

In conclusion, our exploration of the sequence with the first term 24 and the rule "add 4" has yielded a fascinating result. Mandy's claim that no number in this sequence is in the 5 times table has been proven false. We have identified 40 as the first number in the sequence that is indeed a multiple of 5. This journey through the numerical landscape serves as a testament to the power of mathematical inquiry and the potential for unexpected discoveries within seemingly simple systems.