Precalc S1 Review - Arithmetic and Geometric Sequences/Series

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 explicit formula for an arithmetic sequence?

Back

The explicit formula for the n-th term of an arithmetic sequence can be expressed as 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 explicit formula for a geometric sequence?

Back

The explicit formula for the n-th term of a geometric sequence can be expressed as 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 5, 8, 11, 14...?

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

How do you calculate the n-th term of an arithmetic sequence?

Back

To calculate the n-th term, use the formula a_n = a_1 + (n-1)d, substituting a_1 for the first term and d for the common difference.

Front

How do you calculate the n-th term of a geometric sequence?

Back

To calculate the n-th term, use the formula a_n = a_1 * r^(n-1), substituting a_1 for the first term and r for the common ratio.

Front

What is the 5th term of the arithmetic sequence 10, 15, 20...?

Back

The 5th term is 30.

Front

What is the 4th term of the geometric sequence 2, 6, 18...?

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The 4th term is 54.