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 determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between any two consecutive terms is the same.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula is defined as: a₁ = first term; a_n = a_n-1 + d, where d is the common difference.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is defined as: a_n = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

Given the sequence 5, 8, 11, 14, what is the common difference?

Back

The common difference is 3.

Front

If the first term of an arithmetic sequence is 10 and the common difference is -2, what is the 5th term?

Back

The 5th term is 2.

Front

What is the 10th term of the arithmetic sequence defined by a_n = 3n + 2?

Back

The 10th term is 32.

Front

How can you identify a non-arithmetic sequence?

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A non-arithmetic sequence does not have a constant difference between consecutive terms.

Front

What is the explicit formula for the arithmetic sequence 20, 15, 10, 5, ...?

Back

The explicit formula is a_n = -5n + 25.