Problem

Consider the pattern. Determine the number of blocks in the 100th figure. Fig 1 Fig 2 Fig 3

Solution

Step 1 :\(\text{Let's find the pattern of the number of blocks in each figure.}\)

Step 2 :\(\text{In Figure 1, there is 1 block.}\)

Step 3 :\(\text{In Figure 2, there are 3 blocks.}\)

Step 4 :\(\text{In Figure 3, there are 5 blocks.}\)

Step 5 :\(\text{We can see that the number of blocks increases by 2 each time.}\)

Step 6 :\(\text{So, the number of blocks in the nth figure is given by the formula: } n + (n - 1) = 2n - 1\)

Step 7 :\(\text{Now, let's find the number of blocks in the 100th figure.}\)

Step 8 :\(\text{Using the formula, we have: } 2(100) - 1 = 200 - 1 = 199\)

Step 9 :\(\boxed{199}\)

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Source: https://solvelyapp.com/problems/16384/

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