10.2 Arithmetic Sequences

Avery, Harper, and Lily are playing a game where they need to identify arithmetic sequences. Can you help them figure out which of the following is an example of an arithmetic sequence?

• 4, 8, 16, 32, 64

• 1, 2, 4, 7, 11

• 15, 13, 11, 9, 7

• 3, 6, 12, 24, 48

Noah, Oliver, and Nora are playing a game where they have to identify arithmetic sequences. They come across a list of sequences, but one of them is NOT an arithmetic sequence. Can you help them figure out which one it is?

• -7, -13, -19, -25,...

• -10, -6, -2, 2,..

• 6, 8, 10, 12,...

• 3, 15, 75, 375,...

Elijah, Zoe, and Nora are trying to solve a math puzzle. They found the first three terms of an arithmetic sequence as follows:

13, 19, 25, ​ (a)   , (b)  

Can you help them find the next two terms of the sequence?

• 31

• 37

• 36

• 30

• 32

• 38

• 29

Avery, Aria, and Liam are playing a number game. They take turns saying the terms of an arithmetic sequence. So far, they have said the following terms:

3, -4, -11

What are the next two terms that Aria and Liam will say in this sequence?

• -17 and -25

• -18 and -26

• -18 and -25

• -17 and -26

Mason, James, and Elijah are discussing arithmetic sequences. They notice that the difference between two consecutive terms is always the same. They decide to call this difference a (a)   .

• common difference

• Formula

• Common Ratio

• Common Factor

Olivia, Ethan, and Kai are playing a number game. They are trying to find the common difference of the sequence 2, -1, -4, -7,... Can you help them figure it out?

• -3

• -1

• -2

• 3

Anika, Avery, and Emma are on a treasure hunt. They found a mysterious note with a sequence of numbers: 7, 27, 47, 67,...

They realized it's a clue! Can you help them figure out the common difference of this sequence to find the next location?

• 10

• 20

• 3

• -20

Imagine Ava, Harper, and Samuel are in a race. Ava is at the starting line, Harper is a few steps ahead, and Samuel is even further. If we know the distance between each step (d), the position of Ava (a₁), and the number of steps (n), which formula would you use to find the position of the nth runner in this arithmetic sequence?

• a_n = a₁ + (n - 1)d

• a_n = a₁ + (n + 1)d

• a_n = a₁ - (n - 1)d

• a_n = a₁ + -(n + 1)d

Abigail, Aiden, and Mia are on a treasure hunt! They found a mysterious scroll with a sequence of numbers: -6, -14, -22, -30, ...

They figured out that these numbers are clues to open a secret door. Can you help them find out what the first number (a₁) in the sequence is?

• -6

• -14

• -22

• -30

Sophia, Daniel, and Zoe are playing a game of number sequences. They started with the sequence 6, 11, 16, 21. If they continue this pattern, can you help them figure out what the 9^th term will be?