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 that each term increases or decreases by in an arithmetic sequence.

Front

Identify the common difference in the sequence: 3, 7, 11, 15, ...

Back

The common difference is 4.

Front

Is the sequence 24, 15, 6, ... an arithmetic sequence?

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Yes, it is an arithmetic sequence with a common difference of -9.

Front

How do you find the nth term of an arithmetic sequence?

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The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

Find the 10th term of the arithmetic sequence: 2, 5, 8, ...

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The 10th term is 29.

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What is the formula for the sum of the first n terms of an arithmetic sequence?

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The sum S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

Calculate the sum of the first 5 terms of the arithmetic sequence: 1, 4, 7, ...

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The sum is 50.

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What is the 63rd term of the arithmetic sequence: -1, 5, 11, ...?

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The 63rd term is 371.

Front

What is the 59th term of the arithmetic sequence: 26, 17, 8, ...?

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The 59th term is -496.