10. Arithmetic and Geometric Sequences - Explicit Formula

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.

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CCSS.HSF.BF.A.2

Front

How do you find the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence can be expressed as: \( a_n = a_1 + (n - 1) \cdot d \), where \( a_1 \) is the first term and \( d \) is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence 2, 8, 14, 20, ...?

Back

The common difference is 6, calculated as 8 - 2 or 14 - 8.

Tags

CCSS.HSF.BF.A.2

Front

Write the explicit formula for the arithmetic sequence 2, 8, 14, 20, ...

Back

The explicit formula is \( a_n = 2 + 6(n - 1) \).

Tags

CCSS.HSF.BF.A.2

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.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence can be expressed as: \( g_n = g_1 \cdot r^{(n - 1)} \), where \( g_1 \) is the first term and \( r \) is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in the geometric sequence 10, 20, 40, 80, ...?

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The common ratio is 2, calculated as 20 / 10 or 40 / 20.

Tags

CCSS.HSF.BF.A.2

Front

Write the explicit formula for the geometric sequence 10, 20, 40, 80, ...

Back

The explicit formula is \( g_n = 10(2)^{(n - 1)} \).

Tags

CCSS.HSF.BF.A.2

Front

What is the first term of the arithmetic sequence 15, 22, 29, 36, 43, ...?

Back

The first term is 15.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence 15, 22, 29, 36, 43, ...?

Back

The common difference is 7, calculated as 22 - 15.

Tags

CCSS.HSF.BF.A.2