Unit 1 Remediation

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What is the nth term definition for a sequence?

Back

The nth term definition of a sequence is a formula that allows you to find any term in the sequence based on its position (n). For example, for the sequence a(n) = 100 - 5n, n ≥ 0, you can find the value of any term by substituting n with the term's position.

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What is the formula for the nth term of the sequence defined by f(0) = 8 and f(n) = f(n-1) + 7?

Back

The formula for the nth term is f(n) = 8 + 7n, n ≥ 0.

Front

What does the notation f(n) = 300 + 8(n-25) represent?

Back

This notation represents the nth term of a sequence where the first term starts at 300 and increases by 8 for each subsequent term starting from n = 25.

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How do you express the nth term of the sequence g(n) = 6·2^(n-1)?

Back

This expression indicates that the first term of the sequence is 6, and each subsequent term is obtained by multiplying the previous term by 2, starting from n = 1.

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What is the nth term definition for the sequence f(n) = 5·3^(n-1)?

Back

This definition indicates that the first term of the sequence is 5, and each subsequent term is obtained by multiplying the previous term by 3, starting from n = 1.

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Define the term 'sequence' in mathematics.

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A sequence is an ordered list of numbers that follow a specific pattern or rule.

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

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

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

Back

The formula for the nth term of an arithmetic sequence is a(n) = a + (n-1)d, where a is the first term and d is the common difference.

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

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The formula for the nth term of a geometric sequence is a(n) = a * r^(n-1), where a is the first term and r is the common ratio.

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How can you find the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms of an arithmetic sequence can be found using the formula S_n = n/2 * (2a + (n-1)d), where a is the first term and d is the common difference.