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, known as the common difference (d).

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 (r).

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) is found by subtracting any term from the term that follows it: d = a(n+1) - a(n).

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) is found by dividing any term by the previous term: r = a(n+1) / a(n).

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated 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 the formula for the nth term of a geometric sequence?

Back

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

Front

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

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The 5th term is 5 + (5-1) * 3 = 5 + 12 = 17.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

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The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

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Is the sequence 2, 4, 8, 16, ... arithmetic or geometric?

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The sequence is geometric because each term is multiplied by 2 to get the next term.

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Is the sequence 10, 7, 4, 1, ... arithmetic or geometric?

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The sequence is arithmetic because the difference between consecutive terms is -3.