Arithmetic Sequences Flashcard #1

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 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

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

Back

The nth term 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 does a_1 represent in a sequence?

Back

a_1 represents the first term of the sequence.

Front

What is a recursive formula?

Back

A recursive formula defines each term of a sequence using the previous term(s).

Front

Write a recursive formula for the sequence: 2, 5, 8, 11...

Back

a_1 = 2; a_n = a_{n-1} + 3.

Front

Identify the common difference in the sequence: 10, 7, 4, 1...

Back

The common difference is -3.

Front

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

Back

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

Front

If the first term is 4 and the common difference is 2, what is the 5th term?

Back

The 5th term is 12.

Front

What is the common ratio in a geometric sequence?

Back

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