Arithmetic 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 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 n-th term of an arithmetic sequence?

Back

The n-th 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 is the first term of the sequence 3, 7, 11, 15, ...?

Back

The first term is 3.

Front

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

Back

The 25th term is 17.

Front

What is the explicit formula for the n-th term of the sequence 2, 9, 16, 23, ...?

Back

a_n = 2 + 7(n-1).

Front

Given the sequence 25, 21, 17, 13, ..., write the explicit equation that models the sequence.

Back

a_n = 25 - 4(n-1).

Front

If a_14 = 68 and d = 3, what is the first term of the sequence?

Back

The first term is 29.

Front

What is the formula to calculate the common difference?

Back

The common difference d can be calculated as d = a_n - a_(n-1), where a_n is the n-th term and a_(n-1) is the previous term.

Front

How can you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.