Arithmetic and Geometric Sequences

Maya and Benjamin are playing a game with numbers. They have a sequence: {-18, -27, -36, -45, ...}. Can you help them find the common difference in this sequence?

• -9

• -3

• -18

• -27

Aiden and Zoe are playing a number game. They have the sequence {4, 11, 18, 25, ...}. Can you help them determine if this sequence is arithmetic? If yes, what is the common difference?

• Yes, common difference is 7

• No, it is not arithmetic

• Yes, common difference is 4

• Yes, common difference is 11

Zoe and Oliver are playing a game with sequences. They come across the sequence {16, 8, 4, 1, ...}. Zoe asks, "Is this sequence arithmetic? If yes, what is the common difference?" Can you help them figure it out?

• Yes, common difference is -4

• No, it is not arithmetic

• Yes, common difference is -8

• Yes, common difference is -3

Maya and Oliver are playing a game with numbers. They have a sequence of numbers: {-9, -33, -57, -81, ...}. Can you help them find the common difference in this sequence?

• -24

• -9

• -12

• -18

Avery and Aria are playing a game with sequences. They stumbled upon the sequence {1/2, 5/6, 7/6, 3/2, ...}. Can you help them determine if this sequence is arithmetic? If it is, what would be the common difference?

• Yes, common difference is 1/3

• No, it is not arithmetic

• Yes, common difference is 1/6

• Yes, common difference is 1/2

Abigail and Ethan are playing a number game. They have a sequence of numbers: {12, 27, 42, 57, ...}. Can you help them write a rule for this sequence and find out what the 18th term will be?

• a_n = 12 + 15(n-1);

  a₁₈ = 267

• a_n = 12 + 15(n-1);

  a₁₈ = 282

• a_n = 12 + 15(n-1);

  a₁₈ = 252

• a_n = 12 + 15(n-1);

  a₁₈ = 297

James and Hannah are playing a number game. They start with the sequence {29, 9, -11, -31, ...}. Can you help them write a rule for this sequence and find out what the 32nd term will be?

• a_n = 29 - 20(n-1);

  a₃₂ = -591

• a_n = 29 - 20(n-1);

  a₃₂ = -601

• a_n = 20 - 29(n-1);

  a₃₂ = -879

• a_n = 29 - 20(n-1);

  a₃₂ = -621

Ava and Anika are playing a game with numbers. They start with -40 and keep subtracting 4 to get the next number in the sequence. Can you help them write a rule for the sequence {-40, -44, -48, -52, ...} and find out what the 49th term will be?

• a_n = -40 - 4(n-1);

  a₄₉ = -232

• a_n = -40 - 4(n-1);

  a₄₉ = -236

• a_n = -4 - 40(n-1);

  a₄₉ = -1924

• a_n = -40 - 4(n-1);

  a₄₉ = -236

Abigail is on a fitness journey and burns calories in the sequence {349, 357, 365, 373, 381, ...}. Can you figure out the rule for this sequence and help her track her progress?

• a_n = 349 + 8(n-1)

• a_n = 349 + 9(n-1)

• a_n = 349 + 7(n-1)

• a_n = 349 + 6(n-1)

Aria and Maya are playing a number game. They have a sequence of numbers: {50, 39, 28, 17, ...}. Aria asks Maya, "Is this sequence arithmetic? If yes, can you tell me the common difference?" Can you help Maya figure it out?

• Yes, common difference is -11

• No, it is not arithmetic

• Yes, common difference is -10

• Yes, common difference is -12