Arithmetic Sequences and Their Rules

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 nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Front

What is the common difference in the sequence 3, 7, 11, 15?

Back

The common difference is 4, as each term increases by 4.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32, calculated as \( 5 + (10-1) \times 3 = 32 \).

Front

What is the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms can be calculated using the formula: \( S_n = \frac{n}{2} (a_1 + a_n) \) or \( S_n = \frac{n}{2} (2a_1 + (n-1)d) \).

Front

What is the formula for the sum of an arithmetic series?

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The formula for the sum of an arithmetic series is: \( S_n = \frac{n}{2} (a_1 + a_n) \), where \( S_n \) is the sum, \( n \) is the number of terms, \( a_1 \) is the first term, and \( a_n \) is the last term.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

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An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.

Front

If an arithmetic sequence has a first term of 10 and a common difference of -2, what are the first five terms?

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The first five terms are 10, 8, 6, 4, 2.

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What is the 5th term of the arithmetic sequence 2, 5, 8, ...?

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The 5th term is 14, calculated as \( 2 + (5-1) \times 3 = 14 \).

Front

How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.