Sequences Review

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 of a geometric sequence can be expressed as t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

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.

Front

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

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The common difference 'd' can be found by subtracting any term from the subsequent term, d = a(n+1) - a(n).

Front

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

Back

The nth term of an arithmetic sequence can be expressed as a(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is the common ratio in a geometric sequence?

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The common ratio 'r' is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

How do you find the next term in a geometric sequence?

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To find the next term in a geometric sequence, multiply the last known term by the common ratio 'r'.

Front

What is sequence notation?

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Sequence notation is a way to express the terms of a sequence using a formula that defines the nth term.

Front

What is the explicit formula for a geometric sequence with first term 5 and common ratio 2?

Back

The explicit formula is t(n) = 5 * 2^(n-1).

Front

What is the explicit formula for an arithmetic sequence with first term 10 and common difference -3?

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The explicit formula is a(n) = 10 + (n-1)(-3).