Unit 2 : Sequences

Front

What is a sequence in mathematics?

Back

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

Front

What is the general form of a geometric sequence?

Back

A geometric sequence is defined by the formula a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

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

Back

The nth term of an arithmetic sequence can be found using the formula a_n = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the difference between consecutive terms in an arithmetic sequence.

Front

What are the first three terms of the sequence a_n = -40 (1/2)^(n-1)?

Back

-40, -20, -10

Front

How do you calculate the 18th term of the sequence a_n = -3 (2)^(n-1)?

Back

Substituting n=18 into the formula gives a_18 = -3 * (2)^(17) = -393,216.

Front

What is the solution to the inequality -3 - 6(4x + 6) > -111?

Back

x < 3

Front

What is the solution to the equation 3x + 2(4x - 4) = 3?

Back

x = 1

Front

What are the first three terms of the sequence a_n = 12 - 5(n - 1)?

Back

12, 7, 2

Front

What is a recursive sequence?

Back

A recursive sequence is a sequence in which each term is defined as a function of one or more of the preceding terms.