Sequences and Series Review

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?

Back

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 and d is the common difference.

Front

What is a geometric sequence?

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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.

Front

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

Back

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 formula for the sum of the first n terms of an arithmetic series?

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The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the formula for the sum of the first n terms of a geometric series?

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The sum of the first n terms of a geometric series can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio and r ≠ 1.

Front

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

Back

The common difference is 4.

Front

Find the 5th term of the arithmetic sequence: 2, 5, 8, 11...

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The 5th term is 14.

Front

Identify the common ratio in the geometric sequence: 2, 6, 18, 54...

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The common ratio is 3.

Front

What is the 22nd term of the sequence defined by a_1 = 5, a_n = a_{n-1} + 3?

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The 22nd term is 68.