Arithmetic & 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.

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

Identify the common difference in the arithmetic sequence: 2, 5, 8, 11, ...

Back

The common difference is 3.

Front

Identify the common ratio in the geometric sequence: 3, 9, 27, 81, ...

Back

The common ratio is 3.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is tₙ = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is tₙ = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

Find the 10th term of the arithmetic sequence: 4, 10, 16, ...

Back

The 10th term is 64.

Front

Find the 5th term of the geometric sequence: 2, 6, 18, ...

Back

The 5th term is 486.

Front

Determine if the sequence is arithmetic, geometric, or neither: 5, 10, 20, 40, ...

Back

The sequence is geometric.

Front

Determine if the sequence is arithmetic, geometric, or neither: 1, 4, 9, 16, ...

Back

The sequence is neither.