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 can be 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 of an arithmetic sequence can be calculated using the formula: a_n = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

Given the first three terms of an arithmetic sequence, how can you find the next terms?

Back

To find the next terms, add the common difference to the last known term.

Front

What is the common difference in the sequence 5, 10, 15, 20?

Back

The common difference is 5, calculated as 10 - 5 or 15 - 10.

Front

How do you determine if a sequence is arithmetic?

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

Front

What is the 10^th term of the arithmetic sequence 3, 7, 11, 15?

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The 10^th term is 39, calculated using the formula a_n = 3 + (10-1)4.

Front

What is the explicit formula for the n^th term of the sequence 2, 5, 8, 11?

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The explicit formula is a_n = 3n - 1.

Front

If the first term of an arithmetic sequence is 4 and the common difference is 3, what is the 5^th term?

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The 5^th term is 16, calculated as 4 + (5-1)3.

Front

What is the 50^th term of the arithmetic sequence 10, 15, 20, ...?

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The 50^th term is 250, calculated using the formula a_n = 10 + (50-1)5.