Exploring Arithmetic Sequences

What defines an arithmetic sequence?

• A sequence where each term increases by a random value

• A sequence where each term is multiplied by a constant

• A sequence where each term increases or decreases by a fixed number

• A sequence where each term is the square of the previous term

What does 'd' represent in the explicit formula of an arithmetic sequence?

• The index of the term being calculated

• The last term of the sequence

• The difference between consecutive terms

• The first term of the sequence

How do you calculate the seventh term of an arithmetic sequence given the first term and the common difference?

• Divide the first term by the common difference

• Add the first term to six times the common difference

• Multiply the first term by seven

• Subtract the common difference from the first term seven times

What is the first term of an arithmetic sequence if the seventh term is 20 and the common difference is 3?

• 11

• 8

• 5

• 2

In an arithmetic sequence, if the common difference is 3, what is the difference between the 10th and 7th terms?

• 3

• 6

• 9

• 12

What is the common difference in an arithmetic sequence where the first term is 2 and the seventh term is 20?

• 3

• 2

• 5

• 4

What is the explicit formula for an arithmetic sequence where the common difference is negative?

• a_n = a1 + d(n - 1)

• a_n = a1 - d(n + 1)

• a_n = a1 - d(n - 1)

• a_n = a1 / d(n - 1)

What term of the sequence is calculated using the explicit formula a_n = a1 + d(n - 1) when n=10?

• 12th term

• 11th term

• 10th term

• 9th term

If the first term of an arithmetic sequence is 20 and the common difference is -7, what is the third term?

• 27

• 6

• 34

• 13

If the 10th term of a decreasing arithmetic sequence is calculated as -43, what is the common difference?

• -10

• 10

• 7

• -7