Exploring Explicit Formulas for Arithmetic Sequences

The video tutorial explains the difference between sequences and series, focusing on arithmetic sequences where a common difference, denoted as D, is added to each term to get the next. It covers how to calculate this common difference and introduces term notation, such as a sub n, to identify specific terms. The tutorial then generalizes the formula for finding terms in a sequence and derives an explicit formula, a sub n = a sub 1 + D(n-1), to directly calculate any term in the sequence.

What is the main difference between a sequence and a series?

• A sequence is a sum of numbers, while a series is a list of numbers.

• A sequence is a list of numbers, while a series is a sum of numbers.

• A sequence is always finite, while a series is infinite.

• A sequence and a series are the same.

In an arithmetic sequence, what does the common difference (D) represent?

• The number of terms in the sequence.

• The value added to each term to get the next term.

• The difference between the first and last term.

• The sum of all terms in the sequence.

If the common difference (D) is 4, what is the result of 25 minus 21?

• 2

• 3

• 4

• 5

What does 'a sub 1' represent in the notation of sequences?

• The first term of the sequence.

• The sum of the sequence.

• The common difference.

• The last term of the sequence.

How many times do you add the common difference to get to the sixth term from the first term?

• 5 times

• 6 times

• 7 times

• 4 times

What is the general formula to find the nth term in an arithmetic sequence?

• a sub n = a sub 1 + D

• a sub n = a sub 1 + D * (n - 1)

• a sub n = a sub 1 + D * n

• a sub n = a sub 1 * D * (n - 1)

If the first term (a sub 1) is 17 and the common difference (D) is 4, what is the sixth term?

• 33

• 25

• 37

• 29

What is the simplified form of the explicit formula for the given sequence where a sub 1 = 17 and D = 4?

• a sub n = 17 + 4n

• a sub n = 13 + 4n

• a sub n = 17 + 4(n - 1)

• a sub n = 13 + 4(n - 1)

Using the formula a sub n = 13 + 4n, what is the 100th term?

• 421

• 417

• 400

• 413

What is the value of a sub 1 in the sequence where a sub n = 13 + 4n?

• 13

• 17

• 21

• 25