Exploring Arithmetic Sequences and Series

What identifies a sequence as arithmetic?

• The sum of all terms is divisible by the number of terms.

• Each term is the square of the previous term.

• The difference between consecutive terms is constant.

• Each term increases by a set percentage.

What is the explicit formula for an arithmetic sequence where the first term is 15 and the common difference is -4?

• a_n = 15 - 4(n - 1)

• a_n = 15 + (n - 1)/4

• a_n = 15 - 4n

• a_n = 15 + 4(n - 1)

How do you find the 38th term of an arithmetic sequence using its explicit formula?

• Divide the first term by 38.

• Add 38 to the first term.

• Multiply the common difference by 38.

• Substitute 38 for n in the formula.

In an arithmetic sequence, if the common difference is negative, how does the sequence progress?

• Each term is greater than the previous term.

• The sequence remains constant.

• The sequence becomes non-linear.

• Each term is less than the previous term.

What does the explicit formula of an arithmetic sequence represent?

• The sum of the sequence's terms.

• The difference between consecutive terms.

• The nth term of the sequence.

• The average value of the sequence's terms.

What is the formula to calculate the sum of the first n terms in an arithmetic series?

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

• S_n = n * (first term - last term)

• S_n = n * (first term + last term)

• S_n = (first term + last term)/n

If the 8th term of an arithmetic sequence is 77, what is the sum of the first 8 terms?

• 154

• 616

• 336

• 308

How can you determine the number of terms in a series when given the sum?

• Multiply the sum by the first term.

• Divide the sum by the common difference.

• Use the quadratic formula.

• Subtract the first term from the sum.

What is the first term of an arithmetic sequence if the 16th term is calculated using a specific value and common difference?

• Subtract the product of the common difference and 15 from the 16th term.

• Add the common difference to the 16th term.

• Divide the 16th term by the common difference.

• Multiply the 16th term by the common difference.

How do you solve for the first term of an arithmetic sequence when given a term other than the first?

• Divide the given term by its position in the sequence.

• Multiply the given term by the common difference.

• Subtract the product of the common difference and its position from the given term.

• Add the common difference to the given term.