Arithmetic and Geometric Sequences Review

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

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

Back

The nth term (a_n) of an arithmetic sequence 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 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

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) of a geometric sequence 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

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

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Front

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

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The common ratio (r) can be found by dividing any term by the previous term: r = a_(n+1) / a_n.

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

Back

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

Front

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.

Front

If the first term of an arithmetic sequence is 1/2 and the common difference is 1/4, what is the fourth term?

Back

The fourth term is 1.5 (or 3/2).

Front

Identify the sequence: {4, 8, 16, 32, ...}. Is it arithmetic or geometric?

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It is a geometric sequence because each term is multiplied by 2.