Sequences

Question 1

What is a sequence in mathematics?

Answer 1

A sequence is an ordered list of numbers that follow a specific pattern.

Question 2

True or False: A sequence can only contain positive numbers.

Answer 2

False

Question 3

Fill in the blank: The difference between consecutive terms in an arithmetic sequence is called the __________.

Answer 3

common difference

Question 4

What is the nth term formula for an arithmetic sequence?

Answer 4

The nth term is given by a_n = a + (n - 1)d, where ‘a’ is the first term and ‘d’ is the common difference.

Question 5

If the first term of an arithmetic sequence is 3 and the common difference is 5, what is the 4th term?

Answer 5

18

Question 6

What type of sequence has a constant ratio between consecutive terms?

Answer 6

Geometric sequence

Question 7

True or False: In a geometric sequence, the common ratio can be negative.

Answer 7

True

Question 8

What is the formula for the nth term of a geometric sequence?

Answer 8

The nth term is given by a_n = a * r^(n - 1), where ‘a’ is the first term and ‘r’ is the common ratio.

Question 9

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 5th term?

Answer 9

162

Question 10

What is the Fibonacci sequence?

Answer 10

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1.

Question 11

Fill in the blank: The first five terms of the Fibonacci sequence are __________.

Answer 11

0, 1, 1, 2, 3

Question 12

What is the common difference in the arithmetic sequence 7, 10, 13, 16?

Answer 12

3

Question 13

True or False: An arithmetic sequence can be represented graphically as a straight line.

Answer 13

True

Question 14

If a sequence has the terms 1, 4, 9, 16, what type of sequence is it?

Answer 14

It is a sequence of perfect squares.

Question 15

What is the term used for a sequence that does not have a defined pattern?

Answer 15

Random sequence