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 fixed amount added to each term to get the next term in the 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 = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

Given the sequence 2, 9, 16, 23, what is the common difference?

Back

The common difference is 7.

Front

What is the explicit formula for the arithmetic sequence 12, 10, 8, 6?

Back

The explicit formula is a_n = -2n + 14.

Front

Is the sequence 17, 9, 1, -7 arithmetic?

Back

Yes, the sequence is arithmetic because the difference between consecutive terms is constant (-8).

Front

Find the next three terms in the sequence 9, 19, 29, 39.

Back

The next three terms are 49, 59, 69.

Front

What is the recursive formula for the sequence 2, 8, 14?

Back

The recursive formula is: a_n = a_n-1 + 6, with a₁ = 2.

Front

What does the term 'explicit formula' mean in the context of sequences?

Back

An explicit formula provides a direct way to calculate the n^th term of a sequence without needing to know the previous terms.

Front

What is the first term of the arithmetic sequence defined by a_n = 7n - 5?

Back

The first term (a₁) is 2.