May you do number 1 how can I prove n^2+n/2 is another expression based on the pattern of the blocks the sum. In the tile pattern below, the first block arrangementhas 1 block, the second block arrangement has 1 +2 blocks, thethird tile arrangement has 1 + 2+3 blocks.23Assuming the block arrangements grow in the same way,the nth arrangement would have blocks.1. Use the visualization to determine two additional solutionstrategies to determine the sum of the first n naturalnumbers.2. If teaching this task, how would you sequence these threesolution strategies (the original provided and your twostrategies)? Briefly provide rationale for your choices.

In the given sequence, every nth term has 'n' more objects than the last term i.e. the (n-1)th term.…

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May you do number 1 how can I prove n^2+n/2 is another expression based on the pattern of the blocks

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter14: Sequences And Mathematical Induction

Section14.1: Arithmetic Sequences

Problem 75PS

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Question

May you do number 1 how can I prove n^2+n/2 is another expression based on the pattern of the blocks

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.
2
3
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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