Sequences Review (Arithmetic & Geometric Explicit and Recursive)

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

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

Back

Front

Write a recursive formula for the arithmetic sequence: 2, 5, 8, 11,...

Back

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 formula for the nth term of a geometric sequence?

Back

Front

Write a recursive formula for the geometric sequence: 4, 12, 36, 108,...

Back

Front

How do you find the 8th term in a geometric sequence?

Back

Front

What is the common ratio in the geometric sequence: 5, 15, 45, 135,...?

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Front

What is the difference between explicit and recursive formulas?

Back

An explicit formula gives the nth term directly, while a recursive formula defines each term based on the previous term.

Front

Can a recursive formula be used without knowing the previous term?

Back

No, a recursive formula requires knowledge of the previous term to calculate the next term.