Sequences

Front

What is a sequence?

Back

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

Front

Define recursive notation in the context of sequences.

Back

Recursive notation defines each term of a sequence based on the previous term(s).

Front

What is the first term of the sequence {–2, –6, –18, –54, –162 ...}?

Back

The first term, a₁, is -2.

Front

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

Back

Multiply the previous term by the common ratio.

Front

What is the common ratio in the sequence {–2, –6, –18, –54, –162 ...}?

Back

The common ratio is 3.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by aₙ = a₁ + (n-1)d, where d is the common difference.

Front

What is the common difference in the sequence 2, 9, 16, 23, 30,...?

Back

The common difference is 7.

Front

What is the Fibonacci sequence?

Back

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

Front

What is the next term in the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, __?

Back

The next term is 89.

Front

How do you determine the 3rd term of a sequence defined recursively?

Back

Use the recursive formula to calculate the previous terms until you reach the desired term.