Sequences & Series HPC Review

Front

What is a sequence?

Back

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

Front

What is a series?

Back

A series is the sum of the terms of a sequence.

Front

Define convergence in the context of sequences.

Back

A sequence converges if its terms approach a specific value as the number of terms increases.

Front

Define divergence in the context of sequences.

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A sequence diverges if its terms do not approach a specific value as the number of terms increases.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is given by: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in an arithmetic sequence?

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The common difference is the difference between consecutive terms in an arithmetic sequence.

Front

How do you find the nth term of a geometric sequence?

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The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

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

Back

The sum of the first n terms of an arithmetic series is given by: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the formula for the sum of a geometric series?

Back

The sum of the first n terms of a geometric series is given by: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio.

Front

What is the formula for the sum of the first n odd numbers?

Back

The sum of the first n odd numbers is given by: S_n = n^2.