How can I get n^2/2+n/2 based on the pattern of the blocks

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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How can I get n^2/2+n/2 based on the pattern of the blocks
2:14 PM Wed Mar 3
* 100% 4
A bbcsulb.desire2learn.com
Another way to derive an expression for the sum is to visualize
the sum. In the tile pattern below, the first block arrangement
has 1 block, the second block arrangement has 1 + 2 blocks, the
third tile arrangement has 1 + 2 + 3 blocks.
1
Assuming the block arrangements grow in the same way,
the nth arrangement would have blocks.
1. Use the visualization to determine two additional solution
strategies to determine the sum of the first n natural
numbers.
2. If teaching this task, how would you sequence these three
solution strategies (the original provided and your two
strategies)? Briefly provide rationale for your choices.
Transcribed Image Text:2:14 PM Wed Mar 3 * 100% 4 A bbcsulb.desire2learn.com Another way to derive an expression for the sum is to visualize the sum. In the tile pattern below, the first block arrangement has 1 block, the second block arrangement has 1 + 2 blocks, the third tile arrangement has 1 + 2 + 3 blocks. 1 Assuming the block arrangements grow in the same way, the nth arrangement would have blocks. 1. Use the visualization to determine two additional solution strategies to determine the sum of the first n natural numbers. 2. If teaching this task, how would you sequence these three solution strategies (the original provided and your two strategies)? Briefly provide rationale for your choices.
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