Arithmetic and Geometric Sequences

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

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1) \cdot d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: \( a_n = a_1 \cdot r^{(n-1)} \), where \( a_1 \) is the first term, \( r \) is the common ratio, and \( n \) is the term number.

Front

What is the common difference in the sequence 5, 8, 11, 14, ...?

Back

The common difference is 3.

Front

What is the common ratio in the sequence 400, 200, 100, 50, 25, ...?

Back

The common ratio is 0.5.

Front

Determine if the sequence 1, 3, 7, 13, ... is arithmetic, geometric, or neither.

Back

Neither.

Front

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

Back

The explicit formula is \( a_n = a_1 + (n-1) \cdot d \).

Front

What is the explicit formula for the nth term of a geometric sequence?

Back

The explicit formula is \( a_n = a_1 \cdot r^{(n-1)} \).

Front

Find the eighth term of the sequence 3, 6, 12, 24, ...

Back

384.