Section 4.4 - 4.5: 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)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 * 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 8, 7.3, 6.6, 5.9?

Back

The common difference is -0.7.

Front

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

Back

The common ratio is 0.5.

Front

If a_1 = 5 and d = 0.5, what is the 25th term of the arithmetic sequence?

Back

The 25th term is 17.

Front

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

Back

The formula is S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Front

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

Back

The formula is S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.

Front

What is the 38th term of the sequence 26, 22, 18, 14?

Back

The 38th term is -122.