Writing Explicit Equations for Sequences

The video tutorial explains arithmetic and geometric sequences, focusing on identifying patterns and writing explicit equations for each type. It covers the concept of common difference in arithmetic sequences and common ratio in geometric sequences, providing examples and practice problems to illustrate these concepts.

What is the common difference in an arithmetic sequence?

• The product of the first and last term

• The sum of all terms divided by the number of terms

• The difference between any two consecutive terms

• The difference between the first and last term

How do you find the nth term in an arithmetic sequence?

• First term * common difference^n

• First term + (n-1) * common difference

• First term + common difference / n

• First term / (n-1) * common difference

What is the first term of the arithmetic sequence if the nth term is 3 + 5(n-1)?

• 8

• 0

• 3

• 5

What is the common difference in the sequence where the nth term is 7 - 6(n-1)?

• -1

• 6

• -6

• 1

What distinguishes a geometric sequence from an arithmetic sequence?

• It is always decreasing

• It cannot have a common difference

• It only contains positive numbers

• It involves multiplication instead of addition

What is the common ratio in a geometric sequence?

• The difference between any two consecutive terms

• The ratio between any two consecutive terms

• The sum of all terms divided by the number of terms

• The product of the first and last term

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the third term?

• 12

• 9

• 6

• 24

How do you find the nth term in a geometric sequence?

• First term + (n-1) * common ratio

• First term * common ratio^(n-1)

• First term + common ratio^n

• First term * common ratio / n

What is the first term of the geometric sequence if the nth term is 3 * 2^(n-1)?

• 2

• 6

• 3

• 12

What is the common ratio in the sequence where the nth term is 2 * 3^(n-1)?

• 9

• 6

• 2

• 3