Exploring Explicit Formulas for Arithmetic Sequences

Why is the recursive formula considered inefficient for finding larger terms in a sequence?

• It is not a true mathematical formula.

• It uses more memory than explicit formulas.

• It requires calculating all previous terms.

• It only works for small sequences.

What does the explicit formula for an arithmetic sequence allow you to find?

• The sum of the sequence.

• Any term directly without previous terms.

• The common difference only.

• Only the first term of the sequence.

In the explicit formula, what does 'n' represent?

• The total number of terms.

• The term number you are trying to find.

• The first term of the sequence.

• The common difference.

What is the role of 'd' in the explicit formula of an arithmetic sequence?

• It is the number of terms in the sequence.

• It indicates the last term of the sequence.

• It is the common difference between consecutive terms.

• It represents the first term.

What does the term 'a_sub_1' represent in the explicit formula of an arithmetic sequence?

• The number of terms in the sequence.

• The first term of the sequence.

• The common difference.

• The last term of the sequence.

How do you determine the common difference in an arithmetic sequence?

• By dividing the last term by the first term.

• By adding the first two terms.

• By multiplying the first term with the second term.

• By subtracting any term from the next term.

What is the 10th term of the sequence where the first term is -3 and the common difference is -4?

• -43

• -27

• -39

• -31

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

• It increases by the common difference.

• It decreases by the common difference.

• It remains constant.

• It alternates between increasing and decreasing.

If the first term of a sequence is 8.8 and the common difference is 1.2, what is the explicit formula?

• a_n = 8.8 + (n - 1) * 1.2

• a_n = 8.8 * n + 1.2

• a_n = 8.8 / (n - 1) + 1.2

• a_n = 8.8 - (n - 1) * 1.2

What is the 75th term of the sequence with the first term 8.8 and common difference 1.2?

• 85.6

• 105.6

• 89.6

• 97.6