Arithmetic and Geometric 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. This difference is called the common difference.

Front

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

Back

The nth term of an arithmetic sequence 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

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common difference in the sequence: 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

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What is the common ratio in the sequence: 3, 6, 12, 24, ...?

Back

The common ratio is 2, as each term is multiplied by 2 to get the next term.

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Find the 10th term of the arithmetic sequence: 4, 7, 10, ...

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The 10th term is 4 + (10 - 1) * 3 = 4 + 27 = 31.

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Find the 5th term of the geometric sequence: 2, 6, 18, ...

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The 5th term is 2 * 3^(5-1) = 2 * 81 = 162.

Front

What is the explicit formula for the arithmetic sequence: 1, 4, 7, ...?

Back

The explicit formula is a_n = 1 + (n - 1) * 3.

Front

What is the explicit formula for the geometric sequence: 5, 15, 45, ...?

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The explicit formula is a_n = 5 * 3^(n-1).