Exploring Sequences and Series

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

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Define a geometric series and provide an example.

• An example of a geometric series is 2 + 6 + 18 + 54, where the first term is 2 and the common ratio is 3.

• 1 + 2 + 3 + 4, with a common ratio of 1

• 5 + 10 + 20 + 40, where the first term is 5 and the common ratio is 2

• 3 + 9 + 27 + 81, with a common difference of 3

What is the sum of the first 20 terms of the arithmetic series where the first term is 2 and the common difference is 4?

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How do you find the sum of an infinite geometric series?

• S = ar / (1 - r) for |r| > 1

• S = a * (1 - r) for |r| < 1

• S = a + r for |r| < 1

• S = a / (1 - r) for |r| < 1

If the sum of the first n terms of an arithmetic series is given by S_n = 3n^2 + 2n, what is the common difference?

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If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

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Explain the difference between a sequence and a series.

• A sequence is an ordered list of elements; a series is the sum of the elements of a sequence.

• A sequence is a geometric arrangement; a series is a linear arrangement of numbers.

• A sequence is the sum of a series; a series is an unordered list of elements.

• A sequence is a random collection of numbers; a series is a type of sequence.

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

• S_n = a(1 - r^n) / (1 - r)

• S_n = a(1 + r^n) / (1 + r)

• S_n = a(r^n - 1) / (r - 1)

• S_n = a(nr) / (1 - r)

Calculate the 7th term of the sequence defined by the formula a_n = 2n + 1.

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

• a_n = a_1 + (n - 1)d

• a_n = n^2 + a_1

• a_n = a_1 * n + d

• a_n = a_1 - (n + 1)d