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

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

Back

The nth term (a_n) 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 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 a geometric sequence?

Back

The nth term (a_n) 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

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the constant factor by which each term in a geometric sequence is multiplied to get the next term.

Front

Find a_12 of the arithmetic sequence 21, 32, 43, 54, 65, …

Back

a_12 = 21 + (12-1) * 11 = 142.

Front

Determine whether the sequence 64, -48, 36, -27, … is arithmetic or geometric.

Back

The sequence is geometric.

Front

Find a_12 of the geometric sequence -64, 96, -144, 216, …

Back

a_12 = -64 * (3/2)^(11) = 5535.84375.

Front

Determine whether the sequence 24, 32, 40, 48, … is arithmetic or geometric.

Back

The sequence is arithmetic.