the sequence of figures shows a pattern. if the pattern repeats, how many circles will figure 4 have? figure…
the sequence of figures shows a pattern. if the pattern repeats, how many circles will figure 4 have? figure 1 figure 2 figure 3
Answer
Explanation:
Step1: Analyze the pattern
In Figure 1, the number of circles is 4. In Figure 2, the number of circles is 5. In Figure 3, the number of circles is 6. The number of circles in each figure forms an arithmetic - sequence with a first term $a_1 = 4$ and a common difference $d=1$.
Step2: Use the arithmetic - sequence formula
The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Here, $a_1 = 4$, $d = 1$, and $n = 4$. Substitute the values into the formula: $a_4=4+(4 - 1)\times1$.
Step3: Calculate the result
First, calculate the value inside the parentheses: $4+(4 - 1)\times1=4 + 3\times1$. Then, perform the multiplication: $4+3\times1=4 + 3$. Finally, perform the addition: $4 + 3=7$.
Answer:
7