Sequences: 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 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

Define explicit formula in the context of sequences.

Back

An explicit formula defines the nth term of a sequence as a function of n, allowing direct computation of any term without needing to know the previous terms.

Front

Define recursive formula in the context of sequences.

Back

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

Front

What is the common difference in the arithmetic sequence 3, 7, 11, 15, ...?

Back

The common difference is 4.

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54, ...?

Back

The common ratio is 3.

Front

Write the explicit formula for the arithmetic sequence 5, 10, 15, ...

Back

a_n = 5n.

Front

Write the recursive formula for the arithmetic sequence 5, 10, 15, ...

Back

a_1 = 5; a_n = a_{n-1} + 5.

Front

What is the explicit formula for the geometric sequence 4, 12, 36, ...?

Back

a_n = 4 imes 3^{(n-1)}.

Front

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

Back

a_1 = 4; a_n = a_{n-1} imes 3.