Identifying 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

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) is found by subtracting any term from the subsequent term: d = a(n+1) - a(n).

Front

What is the explicit formula for an arithmetic sequence?

Back

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

Front

Given the sequence 2, 8, 14, ..., what is the common difference?

Back

The common difference is 6.

Front

Write the explicit formula for the sequence 2, 8, 14, ...

Back

a_n = 6n - 4.

Front

Given the sequence 25, 21, 17, 13, ..., what is the common difference?

Back

The common difference is -4.

Front

Write the explicit formula for the sequence 25, 21, 17, 13, ...

Back

a_n = -4n + 29.

Front

How do you determine if a sequence is arithmetic?

Back

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

Front

Identify the common difference in the sequence 97, 86, 75, 64, ...

Back

The common difference is -11.

Front

Find the 32nd term of the sequence 9, 4, -1, -6, -11, ...

Back

The 32nd term is -146.