Arithmetic and Geometric Sequences

The video tutorial introduces arithmetic and geometric sequences, explaining their patterns and formulas. Arithmetic sequences have a common difference, while geometric sequences have a common ratio. The video covers recursive and closed formulas for both types, emphasizing the importance of identifying the first term as either a sub zero or a sub one. Examples and informal proofs are provided to illustrate these concepts.

What is the common difference in the sequence 3, 7, 11, 15?

• 4

• 3

• 2

• 5

Which formula represents the nth term of an arithmetic sequence starting with a sub zero?

• a sub n = a + d * n

• a sub n = a * n

• a sub n = a + n

• a sub n = a * r^n

If the first term of an arithmetic sequence is a sub one, what is the closed formula for the nth term?

• a sub n = a sub one * n

• a sub n = a sub one + d * (n - 1)

• a sub n = a sub one * d^n

• a sub n = a sub one + d * n

What is the common ratio in the sequence 3, 12, 48, 192?

• 4

• 3

• 5

• 2

Which formula represents the nth term of a geometric sequence starting with a sub zero?

• a sub n = a * r^n

• a sub n = a + d * n

• a sub n = a + n

• a sub n = a * n

If the first term of a geometric sequence is a sub one, what is the closed formula for the nth term?

• a sub n = a sub one + n

• a sub n = a sub one + r * n

• a sub n = a sub one * n

• a sub n = a sub one * r^(n - 1)

How do you find the common ratio in a geometric sequence?

• Subtract consecutive terms

• Divide a term by the previous term

• Multiply consecutive terms

• Add consecutive terms

What is the main difference between arithmetic and geometric sequences?

• Both have a common difference

• Arithmetic sequences have a common difference, geometric sequences have a common ratio

• Both have a common ratio

• Arithmetic sequences have a common ratio, geometric sequences have a common difference

Which sequence is defined by multiplying each term by a constant to get the next term?

• Arithmetic sequence

• Geometric sequence

• Fibonacci sequence

• Harmonic sequence

What is emphasized about the first term in both arithmetic and geometric sequences?

• It is always the largest term

• It determines the formula used

• It must always be zero

• It is always the smallest term