Arithmetic or Geometric?

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

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. For example, 2, 6, 18, 54 is a geometric sequence with a common ratio of 3.

Front

Identify the common difference in the sequence: 4, 7, 10, 13.

Back

The common difference is 3.

Front

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

Back

The common ratio is 3.

Front

What is the formula for 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)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for 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 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Determine if the sequence −1, −5, −25, −125 is arithmetic, geometric, or neither.

Back

The sequence is geometric.

Front

Determine if the sequence 2, 5, 8, 11 is arithmetic, geometric, or neither.

Back

The sequence is arithmetic.

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum of the first n terms (S_n) of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum of the first n terms (S_n) of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio.