Understanding Sequences

This video tutorial by Monica Wama covers the basics of sequences, including finite and infinite sequences. It explains how to identify patterns in sequences and derive mathematical expressions or rules for generating them. The video also discusses sequence terms, their order, and how to solve problems using general terms. Additionally, it provides examples of finding general terms for given sequences, emphasizing the importance of pattern recognition and mathematical reasoning.

What is the pattern in the sequence: A, B, G, J?

• Skip two letters

• Skip one letter

• Skip four letters

• Skip three letters

How is a finite sequence different from an infinite sequence?

• A finite sequence has only even numbers, while an infinite sequence has odd numbers.

• A finite sequence is always decreasing, while an infinite sequence is not.

• A finite sequence is always increasing, while an infinite sequence is not.

• A finite sequence has a last term, while an infinite sequence does not.

In the sequence 1, 3, 6, 10, 15, what is the 5th term?

• 10

• 18

• 12

• 15

What is the general term for the sequence 1, 4, 9, 16, 25?

• n+1

• n^2

• n^3

• 2n

If a sequence is defined by a_n = (n-3)^n, what is the first term?

• 0

• -2

• 1

• 2

For the sequence defined by a_n = (-1)^n / (2n - 1), what is the 20th term?

• 1/40

• -1/40

• -1/39

• 1/39

What is the general term for the sequence 1, 1/2, 1/3, 1/4, 1/5?

• n^2

• 1/n^2

• n/1

• 1/n

In the sequence -5, 10, -15, 20, -25, what is the pattern?

• Decreasing by 5

• Increasing by 5

• Alternating signs with multiples of 10

• Alternating signs with multiples of 5

What is the general term for the sequence 1, 8, 27, 64, 125?

• 3^n

• 2^n

• n^3

• n^2

For the sequence 3, -6, 9, -12, 15, what is the general term?

• 3n

• (-1)^n * n^2

• (-1)^n * 3n

• n^3