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 in the sequence.

Front

What is the formula for the n-th term of an arithmetic sequence?

Back

The n-th term (a_n) of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

Is the sequence 2, 4, 6, 8, ... arithmetic?

Back

Yes, the sequence is arithmetic with a common difference of 2.

Front

What is the common difference in the sequence 10, 7, 4, 1, ...?

Back

The common difference is -3.

Front

Can a sequence be arithmetic if the common difference is zero?

Back

Yes, a sequence can be arithmetic with a common difference of zero; it would consist of the same repeated number.

Front

What is the explicit formula for the arithmetic sequence 5, 10, 15, ...?

Back

The explicit formula is a_n = 5 + (n - 1)5.

Front

How can you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant.

Front

What is the common difference in the sequence 100, 90, 80, ...?

Back

The common difference is -10.

Front

Is the sequence 1, 2, 4, 8, ... arithmetic?

Back

No, the sequence is not arithmetic; it is geometric.