Fast & Furious part 6: Explicit & Recursive Sequences

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

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

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

How do you find the common difference of an arithmetic sequence?

Back

To find the common difference, subtract any term from the previous term (d = a_n - a_(n-1)).

Front

What is an explicit formula for a sequence?

Back

An explicit formula defines the nth term of a sequence as a function of n, allowing direct computation of any term.

Front

What is a recursive formula for a sequence?

Back

A recursive formula defines each term of a sequence based on the previous term(s), requiring knowledge of earlier terms to find later ones.

Front

Write the explicit formula for the geometric sequence: 3, 6, 12, 24...

Back

a_n = 3(2)^(n-1) where the common ratio is 2.

Front

Write the recursive rule for the arithmetic sequence: 5, 8, 11, 14...

Back

a_1 = 5; a_n = a_(n-1) + 3.