We are given three figures that show a dot pattern.
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Note that each new figure has 2 more dots than the previous figure. Then, Figure 4 will have 2 more dots than Figure 3. The same will occur with Figure 5 — we will add two dots to Figure 4 to get the sketch of Figure 5.
Let's look at the given dot pattern again.
We can write this pattern using addition.
Fig. 1:& 4
Fig. 2:& 4+2=6
Fig. 3:& 4+2+2=8
Fig. 4:& 4+2+2+2=10
Fig. 5:& 4+2+2+2+2=12
The number 2 is repeated. We can rewrite it as the product of 2 and the number of times it is repeated in the sum.
Fig. 1:& 4+2(0)=4
Fig. 2:& 4+2(1)=6
Fig. 3:& 4+2(2)=8
Fig. 4:& 4+2(3)=10
Fig. 5:& 4+2(4)=12
Notice that the number inside the parentheses is always 1 unit less than the number of the figure. We can use n to represent the number of the figure and n-1 to represent the number inside the parentheses.
Fig. n: 4+2(n-1)
This expression will help us to determine the number of dots in any figure. We only need to substitute the value of n by the number of the wanted figure and evaluate the expression to obtain the number of dots. Let's try it with n= 5.
We want to determine if there is a figure with exactly 38 dots. To do so, we can use the expression found in Part B.
Fig. n: 4+2(n-1)
This expression gives us the number of dots in figure number n. Then, we can equate this expression to 38 to find if there is a figure with exactly 38 dots.
4+2(n-1)=38
Since n is the number of the figure, we can solve this equation for n to find the number of the figure that will have 38 dots.
