Geometric Sequences

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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.

Tags

CCSS.HSF.BF.A.2

Front

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

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The nth term of a geometric sequence can be found using the formula: t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

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What is the recursive formula for a geometric sequence?

Back

The recursive formula for a geometric sequence is: a(n) = a(n-1) * r, where 'r' is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

Given the sequence: 3, 6, 12, 24, ..., what is the common ratio?

Back

The common ratio is 2.

Tags

CCSS.HSF.BF.A.2

Front

Given the sequence: 81, 27, 9, 3, ..., write the explicit rule.

Back

The explicit rule is t(n) = 81 * (1/3)^(n-1).

Tags

CCSS.HSF.BF.A.2

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What is the 5th term of the sequence: 5, 10, 20, 40, ...?

Back

The 5th term is 80.

Tags

CCSS.HSF.BF.A.2

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If the first term of a geometric sequence is 10 and the common ratio is 2, what is the 4th term?

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The 4th term is 80.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula to find the sum of the first n terms of a geometric sequence?

Back

The sum of the first n terms (S_n) of a geometric sequence is given by: S_n = a * (1 - r^n) / (1 - r), where 'a' is the first term and 'r' is the common ratio.

Tags

CCSS.HSA.SSE.B.4

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What is the 11th term of the sequence: 64, -32, 16, -8, ...?

Back

The 11th term is 0.0625.

Tags

CCSS.HSF.BF.A.2