Exploring Arithmetic Sequences and Series

What is the common difference in the sequence 5, 11, 17, 23, 29?

• 4

• 6

• 7

• 5

Which formula type allows you to determine any term given the previous term?

• Explicit

• Differential

• Recursive

• Linear

What is the explicit formula for an arithmetic sequence starting at 5 with a common difference of 6?

• a_n = 6n + 5

• a_n = 5n + 6

• a_n = 5 + (n-1) * 6

• a_n = 5 + 6n

How is an arithmetic sequence related to a linear function?

• It is a type of linear function with domain as natural numbers.

• It is a quadratic function.

• It is not related to linear functions.

• It is a type of exponential function.

What was the sum calculated by young Gauss for the series from 1 to 100?

• 5500

• 5150

• 5000

• 5050

What is the formula for the sum of an arithmetic series?

• Sum = n/2 * (first term + last term)

• Sum = n * (first term + last term)

• Sum = n * (first term - last term)

• Sum = (first term + last term) / n

If the first term of an arithmetic sequence is 42 and the sixth term is 27, what is the common difference?

• 3

• 5

• -5

• -3

Using Gauss's approach, how would you calculate the sum of the series from 1 to n?

• n/2 * (1 + n)

• n * (1 + n)

• n/2 * (n - 1)

• (1 + n)/2

What is the sum of the first 10 terms of an arithmetic sequence starting at 3 with a common difference of 2?

• 95

• 105

• 110

• 100

How does the formula for the sum of an arithmetic series adjust for odd n?

• It works the same as for even n.

• It cannot sum odd n.

• It doubles the last term.

• It only sums up to n-1.