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.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers in which 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 sequence: 5, 8, 11, 14.

Back

The common difference is 3.

Front

Identify the common ratio in the sequence: 3, 6, 12, 24.

Back

The common ratio is 2.

Front

What is the nth term formula for an arithmetic sequence?

Back

The nth term formula is: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the nth term formula for a geometric sequence?

Back

The nth term formula is: 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 2, 4, 8, 16 is arithmetic or geometric.

Back

The sequence is geometric.

Front

Determine if the sequence 10, 7, 4, 1 is arithmetic or geometric.

Back

The sequence is arithmetic.

Front

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

Back

The sum is given by S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms.

Front

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

Back

The sum is given by S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.