Arithmetic Sequences and Formulas

The video tutorial covers arithmetic sequences, focusing on the explicit formula. It explains how to use the formula to find any term in a sequence without calculating previous terms. Several examples demonstrate the process, including sequences with positive, negative, and complex common differences. The tutorial also includes a real-world application and a conversion from a recursive to an explicit formula.

What is the main advantage of using an explicit formula in arithmetic sequences?

• It requires less memory to store.

• It can only be used for sequences with positive terms.

• It allows finding any term without computing previous terms.

• It is easier to understand than recursive formulas.

Which two components are necessary to write an explicit formula for an arithmetic sequence?

• The number of terms and the sum of the sequence

• The first term and the last term

• The last term and the common ratio

• The first term and the common difference

If the first term of a sequence is 7 and the common difference is 6, what is the explicit formula?

• a_n = 7n - 6

• a_n = 7n + 6

• a_n = 6n - 7

• a_n = 6n + 1

How do you find the 23rd term of a sequence using the formula a_n = 6n + 1?

• 23 times 6 minus 1

• 6 times 23 plus 1

• 23 plus 6 times 1

• 6 plus 23 times 1

What is the common difference in the sequence where the first term is -13 and the second term is -11?

• 2

• -2

• 3

• -3

In the sequence where the first term is 2 and the common difference is -9, what is the explicit formula?

• a_n = 9n + 11

• a_n = -9n - 11

• a_n = 9n - 11

• a_n = -9n + 11

If Callie starts with 27 stickers and adds 25 each year, what will be the seventh term in the sequence?

• 177

• 152

• 202

• 127

What is the common difference in the sequence where the first term is 10 and the second term is 7.5?

• 2.5

• -3.5

• -2.5

• 3.5

How can you convert a recursive formula to an explicit formula?

• By using the number of terms

• By using the first term and the common difference

• By using the last term and the common ratio

• By using the sum of the sequence

What is the explicit formula for a sequence with a first term of 6 and a common difference of 3.2?

• a_n = 3.2n + 2.8

• a_n = 6n + 3.2

• a_n = 3.2n - 6

• a_n = 6n - 3.2