Q: What is the value of the 10th term in the sequence for the number of dots in the designs?

$$a_{10} = 2 + 3 \times 9 = 29$$

Q: If the pattern continues, how many dots will be in design 15?

$$a_{15} = 2 + 3 \times 14 = 44$$

Q: If the sequence continues, what is the difference in the number of dots between design 12 and design 7?

$$[2 + 3 \times 11] - [2 + 3 \times 6] = 35 - 20 = 15$$

Question 1

Given the sequence representing the number of dots in each design: 2, 5, 8, 11, ..., what is the formula for the $$nth $$term of the sequence?

Accepted Answer

$$a_n = 2 + 3(n-1)$$

Question 2

What is the value of the 10th term in the sequence for the number of dots in the designs?

Accepted Answer

$$a_{10} = 2 + 3 	imes 9 = 29$$

Question 3

If the pattern continues, how many dots will be in design 15?

Accepted Answer

$$a_{15} = 2 + 3 	imes 14 = 44$$

Question 4

Which of the following best describes the sequence of the number of dots in the designs?

Accepted Answer

It is an arithmetic sequence with a common difference of 3.

Question 5

If the first term of a sequence is 2 and the common difference is 3, what is the sum of the first 4 terms?

Accepted Answer

$$S_4 = 2 + 5 + 8 + 11 = 26$

Question 6

Which equation would you use to find the number of dots in the $$nth $$design if the first term is $$a_1 = 2$ and the common difference is d = 3$?

Accepted Answer

$$a_n = a_1$ + (n-1)d$$

Question 7

A student claims that the 8th design will have 24 dots. What mistake did the student most likely make?

Accepted Answer

They used the wrong formula for the $$nth $$term.

Question 8

If you were to graph the design number ($$n) on $$the $$x-$$axis and the number of dots on the $$y-$$axis, what type of graph would you expect?

Accepted Answer

A straight line with a positive slope.

Question 9

Suppose a new design is created by doubling the number of dots in each design. How many dots will be in the 4th new design?

Accepted Answer

$$2 	imes 11 = 22$$

Question 10

In a real-world context, if each dot represents a light bulb in a decorative pattern, and each bulb costs $0.50, how much would it cost to create design 8?

Accepted Answer

$$23 	imes 0.50 = 11.50$$

Question 11

If the sequence continues, what is the difference in the number of dots between design 12 and design 7?

Accepted Answer

$$[2 + 3 	imes 11] - [2 + 3 	imes 6] = 35 - 20 = 15$$

Question 12

If the pattern is used to design a necklace and each dot represents a bead, how many beads are needed for the first 5 designs combined?

Accepted Answer

$$2 + 5 + 8 + 11 + 14 = 40$$

Arithmetic Sequences: Dot Patterns and Formula Application

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