Question

A geometric sequence g starts 1,3...a. write a recursive definition for this sequence using function notation.b. sketch a graph of the first 5 terms of g​

Answer 1

A recursive definition for a geometric sequence can be written using function notation. The sequence starts with 1,3, and the recursive definition is a₁ = 1 and aₙ = r * aₙ₋₁. To sketch the graph of the first 5 terms, plot the terms on a number line.

Step-by-step explanation:

A recursive definition for a geometric sequence can be written using function notation. In this case, the sequence starts with 1,3, so we can say that the first term (a₁) is 1 and the common ratio (r) is 3. The recursive definition can be written as:

a₁ = 1

aₙ = r * aₙ₋₁

where aₙ represents the nth term of the sequence and aₙ₋₁ represents the (n-1)th term.

To sketch a graph of the first 5 terms of the sequence, we can plot the terms on a number line. The first term is 1, the second term is 3, the third term is 9 (3 * 3), the fourth term is 27 (3 * 9), and the fifth term is 81 (3 * 27).