1 exploration: describing a pattern (continued)\n\nc. n = 1 n = 2 n = 3 n = 4 n = 5\n\nnumber of rows, n 1 2…

1 exploration: describing a pattern (continued)\n\nc. n = 1 n = 2 n = 3 n = 4 n = 5\n\nnumber of rows, n 1 2 3 4 5\nnumber of dots, y \n\ncommunicate your answer\n2. how can you use an arithmetic sequence to describe a pattern? give an example from real life.\n3. in chemistry, water is called h₂o because each molecule of water has two hydrogen atoms and one oxygen atom. describe the pattern shown below. use the pattern to determine the number of atoms in 23 molecules.\n n = 1 n = 2 n = 3 n = 4 n = 5

1 exploration: describing a pattern (continued)\n\nc. n = 1 n = 2 n = 3 n = 4 n = 5\n\nnumber of rows, n 1 2 3 4 5\nnumber of dots, y \n\ncommunicate your answer\n2. how can you use an arithmetic sequence to describe a pattern? give an example from real life.\n3. in chemistry, water is called h₂o because each molecule of water has two hydrogen atoms and one oxygen atom. describe the pattern shown below. use the pattern to determine the number of atoms in 23 molecules.\n n = 1 n = 2 n = 3 n = 4 n = 5

Answer

1. Filling the table for dot - pattern

Explanation:

Step1: Count dots for (n = 1)

For (n=1), there are 2 dots. So when (n = 1), (y=2).

Step2: Count dots for (n = 2)

For (n = 2), there are 4 dots. So when (n = 2), (y = 4).

Step3: Count dots for (n = 3)

For (n=3), there are 6 dots. So when (n = 3), (y = 6).

Step4: Count dots for (n = 4)

For (n = 4), there are 8 dots. So when (n = 4), (y = 8).

Step5: Count dots for (n = 5)

For (n=5), there are 10 dots. So when (n = 5), (y = 10).

Answer:

Number of rows, (n) 1 2 3 4 5
Number of dots, (y) 2 4 6 8 10

2. Using arithmetic sequence to describe a pattern

Brief Explanations:

An arithmetic sequence has a common difference between consecutive terms. For example, in the cost of buying stamps. If one - stamp costs $0.50, the cost of 2 stamps is $1.00, 3 stamps is $1.50. The sequence of costs (0.5,1.0,1.5,\cdots) has a common difference of $0.50. The general formula for an arithmetic sequence is (a_n=a_1+(n - 1)d), where (a_1) is the first - term and (d) is the common difference.

Answer:

An arithmetic sequence can be used to describe patterns where there is a constant increase or decrease between consecutive terms. For example, the cost of buying stamps where each stamp costs a fixed amount.

3. Number of atoms in water molecules

Explanation:

Step1: Determine number of atoms in one molecule

One molecule of water ((H_2O)) has (2 + 1=3) atoms.

Step2: Find general formula for number of atoms in (n) molecules

The number of atoms in (n) molecules of water follows a pattern where the number of atoms (A = 3n).

Step3: Calculate number of atoms in 23 molecules

Substitute (n = 23) into the formula (A=3n). So (A=3\times23 = 69).

Answer:

The pattern is that the number of atoms in (n) molecules of water is given by the formula (A = 3n). The number of atoms in 23 molecules of water is 69.