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Arithmetic vs. Geometric: What is the key difference in how terms change?

Arithmetic: Constant addition/subtraction (common difference) | Geometric: Constant multiplication/division (common ratio)

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Arithmetic vs. Geometric: What is the key difference in how terms change?

Arithmetic: Constant addition/subtraction (common difference) | Geometric: Constant multiplication/division (common ratio)

Compare the growth patterns of arithmetic and geometric sequences.

Arithmetic: Linear growth | Geometric: Exponential growth

What is an arithmetic sequence?

A sequence where the difference between consecutive terms is constant.

What is a geometric sequence?

A sequence where the ratio between consecutive terms is constant.

Define common difference.

The constant difference between consecutive terms in an arithmetic sequence.

Define common ratio.

The constant ratio between consecutive terms in a geometric sequence.

What are discrete points in the context of sequences?

Isolated points on a graph, representing terms of a sequence, not connected by a continuous line.

What is a sequence?

An ordered list of numbers, where each number has a specific position.

Arithmetic sequence: Formula for the nth term (given initial term).

$a_n = a_0 + dn$

Arithmetic sequence: Formula for the nth term (given a known term).

$a_n = a_k + d(n-k)$

Geometric sequence: Formula for the nth term (given initial term).

$g_n = g_0 * r^n$

Geometric sequence: Formula for the nth term (given a known term).

$g_n = g_k * r^(n-k)$

All Flashcards

Arithmetic vs. Geometric: What is the key difference in how terms change?

Arithmetic: Constant addition/subtraction (common difference) | Geometric: Constant multiplication/division (common ratio)

Compare the growth patterns of arithmetic and geometric sequences.

Arithmetic: Linear growth | Geometric: Exponential growth

What is an arithmetic sequence?

A sequence where the difference between consecutive terms is constant.

What is a geometric sequence?

A sequence where the ratio between consecutive terms is constant.

Define common difference.

The constant difference between consecutive terms in an arithmetic sequence.

Define common ratio.

The constant ratio between consecutive terms in a geometric sequence.

What are discrete points in the context of sequences?

Isolated points on a graph, representing terms of a sequence, not connected by a continuous line.

What is a sequence?

An ordered list of numbers, where each number has a specific position.

Arithmetic sequence: Formula for the nth term (given initial term).

$a_n = a_0 + dn$

Arithmetic sequence: Formula for the nth term (given a known term).

$a_n = a_k + d(n-k)$

Geometric sequence: Formula for the nth term (given initial term).

$g_n = g_0 * r^n$

Geometric sequence: Formula for the nth term (given a known term).

$g_n = g_k * r^(n-k)$